Analytic Geometry
Distance Formula: CLASSWORK
1. Find the distance between (-9, 1) & (-5, -2)
2. Find the distance between (10, 3) & (1, -3)
̅̅̅̅ = ?
3. Length of 𝐵𝐷
̅̅̅̅ = ?
4. Length of 𝐴𝐷
#3 - 5
̅̅̅̅ = ?
5. Length of 𝐷𝐶
Distance Formula: HOMEWORK
6. Find the distance between (2, 9) & (-3, 14)
7. Find the distance between (-3, 2) & (9, 7)
8. length of ̅̅̅̅
𝐴𝐷 = ?
9. length of ̅̅̅̅
𝐵𝐷 = ?
#8 - 10
10. length of ̅̅̅̅
𝐶𝐷 = ?
Geometry – Analytic Geometry
~1~
NJCTL.org
Midpoint Formula: CLASSWORK
Calculate the coordinates of the midpoint of the given segments
11. (0, 0), (6, 10)
14. (-3, 8), (13, -6)
12. (2, 3), (6, 7)
15. (-1, -14), (-2, -6)
13. (4, -1), (-2, 5)
16. (3, 2), (6, 6)
17. (-5, 2), (0, 4)
Calculate the coordinates of the other endpoint of the segment with the given endpoint and midpoint M
18. endpoint: (4,6), midpoint: (7,11) 19. endpoint: (2, 6), midpoint:
20. endpoint: (3, -12), midpoint (2,(-1, 1)
1)
Midpoint Formula: HOMEWORK
Calculate the coordinates of the midpoint of the given segments
21. (0, 0), (8, 4)
24. (6, 0), (2, 7)
22. (-1, 3), (7, -1)
25. (-5, -3), (-3, -5)
23. (3, 5), (7, -9)
26. (13, 8), (-6, -6)
27. (-4, -2), (1, 3)
Calculate the coordinates of the other endpoint of the segment with the given endpoint and midpoint M
28. endpoint: (-5, 9)
29. endpoint: (6, 7)
30. endpoint: (2, 4)
midpoint (-8, -2)
midpoint (10, -7)
midpoint (-1, 7)
Geometry – Analytic Geometry
~2~
NJCTL.org
Partitions of a Line Segment: CLASSWORK
PARCC-type Questions:
31. Line segment AB in the coordinate plane has endpoints with coordinates A (3, -10) and B(-6, -1).
̅̅̅̅
a) Graph 𝐴𝐵
b) Find 2 possible locations for point C so that C divides ̅̅̅̅
𝐴𝐵 into 2 parts with lengths in a ratio of 1:2.
32. Line segment EF in the coordinate plane has endpoints with coordinates E (-10, 11) and F (5, -9).
a) Graph ̅̅̅̅
𝐸𝐹
b) Find 2 possible locations for point G so that G divides ̅̅̅̅
𝐸𝐹 into 2 parts with lengths in a ratio of 2:3.
3
33. Line segment JK in the coordinate plane has endpoints with coordinates J (11, 11) and K (-10, -10). Find
̅̅̅ into two parts with lengths in a ratio of 3:4.
two possible locations for point P that divides 𝐽𝐾
34. Line segment LM in the coordinate plane has endpoints with coordinates L (-12, 10) and M (6, -8). Find
̅̅̅̅ into two parts with lengths in a ratio of 2:7.
two possible locations for point P that divides 𝐿𝑀
35. Line segment RS in the coordinate plane has endpoints with coordinates R(7, -11) and S(-9, 13). Find two
possible locations for point P that divides ̅̅̅̅
𝑅𝑆 into two parts with lengths in a ratio of 3:5.
Partitions of a Line Segment: HOMEWORK
PARCC-type Questions:
36. Line segment AB in the coordinate plane has endpoints with coordinates A (5, -7) and B(-10, 3).
a) Graph ̅̅̅̅
𝐴𝐵
b) Find 2 possible locations for point C so that C divides ̅̅̅̅
𝐴𝐵 into 2 parts with lengths in a ratio of 1:4.
4
37. Line segment EF in the coordinate plane has endpoints with coordinates E (-10, 11) and F (10, -9).
̅̅̅̅
a) Graph 𝐸𝐹
b) Find 2 possible locations for point G so that G divides ̅̅̅̅
𝐸𝐹 into 2 parts with lengths in a ratio of 7:3.
38. Line segment JK in the coordinate plane has endpoints with coordinates J (11, 11) and K (-10, -10). Find
̅̅̅ into two parts with lengths in a ratio of 2:5.
two possible locations for point P that divides 𝐽𝐾
39. Line segment LM in the coordinate plane has endpoints with coordinates L (-12, 10) and M (6, -8). Find
̅̅̅̅ into two parts with lengths in a ratio of 5:4.
two possible locations for point P that divides 𝐿𝑀
40. Line segment RS in the coordinate plane has endpoints with coordinates R(7, -11) and S(-9, 13). Find two
possible locations for point P that divides ̅̅̅̅
𝑅𝑆 into two parts with lengths in a ratio of 1:7.
5
Slopes of Parallel & Perpendicular Lines: CLASSWORK
Identify the slope of the line containing the given points:
41. (-2,11), (-5, 2)
42. (-4,11), (-4, -7)
43. (-2,22), (-5, 22)
44. Is the following system of equations parallel? Justify your answer.
A
B
45. Is the following system of equations perpendicular? Justify your answer.
A
B
46. If one line has a slope of -5, what must be the slope of a line parallel to it?
47. If one line passes through the points (-1, 2) & (7, 6), what must be the slope of a line parallel
to it?
48. If one line passes through the points (3, -5) & (1, 9) and a parallel line passes through the
point (3, 4), what is the other point that would lie on the 2nd line?
6
49. If one line has a slope of ½, what must be the slope of a line perpendicular to it?
50. If one line passes through the points (3, -5) & (1, 9), what must be the slope of a line
perpendicular to it?
51. If one line passes through the points (5, 2) & (7, 6) and a perpendicular line passes through
the point (3, 4), what is the other point that would lie on the 2nd line?
Slopes of Parallel & Perpendicular Lines: HOMEWORK
Identify the slope of the line containing the given points:
52. (-6,12), (-2, 5)
53. (14,11), (-14, 11)
54. (-2,17), (-2, 18)
55. Is the following system of equations parallel? Justify your answer.
A
B
56. Is the following system of equations perpendicular? Justify your answer.
A
B
7
57. If one line has a slope of ½, what must be the slope of a line parallel to it?
58. If one line passes through the points (3, -5) & (1, 9), what must be the slope of a line parallel
to it?
59. If one line passes through the points (5, 2) & (7, 6) and a parallel line passes through the
point (3, 4), what is another point that would lie on the 2nd line?
60. If one line has a slope of -5, what must be the slope of a line perpendicular to it?
61. If one line passes through the points (-1, 2) & (7, 6), what must be the slope of a line
perpendicular to it?
62. If one line passes through the points (3, -5) & (1, 9) and a perpendicular line passes through
the point (3, 4), what is another point that would lie on the 2nd line?
Equations of Parallel & Perpendicular Lines: CLASSWORK
63. Find an equation of the line in point-slope form passing through point (-2, 5) and parallel to
the line whose equation is 4x – 2y = -5
64. Two lines are represented by equations: 2x + 4y = 21 and y = kx – 12. What value of k will
make lines parallel?
65. Find an equation of the line in slope-intercept form passing through point (-4,6) and parallel
to the line whose equation is y = -¾ x + 11
66. The sides of a quadrilateral lie on the lines y = 4x + 5, y = 1/3x +7, 8x – 2y = 1, and
x – 3y = 2. Is the quadrilateral a parallelogram? Justify your answer.
67. Find an equation of the line passing through point (4, -5) and perpendicular to the line whose
equation is 3x – 6y = -11.
68. Two lines are represented by equations: -3x + 6y =21 and y = kx +5. What value of k will
make lines perpendicular?
69. Find an equation of the line passing through point (8, -2) and perpendicular to the line whose
equation is y = 4x + 11.
70. The sides of a quadrilateral lie on the lines y= 4x + 5, y = 1/3x + 7, x + 4y = 1, and
x – 3y = 2, is the quadrilateral a rectangle? Justify your answer.
71. Determine if the following equations are parallel, perpendicular, or neither. Justify your
answer.
4x + 3y = 9
6x – 8y = 20
8
72. Determine if the following equations are parallel, perpendicular, or neither. Justify your
answer. 5(x + 3) = 3y + 12
5x + 3y = 15
Equations of Parallel & Perpendicular Lines: HOMEWORK
73. Find an equation of the line in point-slope form passing through point (-3, 2) and parallel to
the line whose equation is 6x – 2y = 7.
74. Two lines are represented by equations: -4x + 12y = 21 and y = kx – 12.
What value of k will make lines parallel?
75. Find an equation of the line in point-slope form passing through point (-8,3) and parallel to
the line whose equation is y = -¾ x + 11.
76. The sides of a quadrilateral lie on the lines 3x + y = 7, x + y = 12, 6x – 2y = 2, and x – y = 2.
Is the quadrilateral a parallelogram? Justify your answer.
77. Find an equation of the line passing through point (-6,2) and perpendicular to the line whose
equation is 4x + 6y = -1
78. Two lines are represented by equations: 10x – 15y = 21 and y = kx + 5.
What value of k will make lines perpendicular?
79. Find an equation of the line passing through point (8,-2) and perpendicular to the line whose
equation is y = -2x + 11
80. The sides of a quadrilateral lie on the lines 4x – y = 5, x + 4y = 7, 8x – 2y = 1, and
3x + 12y = 2. Is the quadrilateral a rectangle? Justify your answer.
81. Determine if the following equations are parallel, perpendicular, or neither. Justify your
answer.
9x + 5y = 32
4.5x + 2.5y = 7.5
82. Determine if the following equations are parallel, perpendicular, or neither. Justify your
answer.
7(x – 1) = 3y + 21 3.5x + 1.5y = 4.5
9
Triangle Coordinate Proofs: CLASSWORK – CP
For numbers 83 – 84 find (a.) the length of AB and (b.) the midpoint coordinates of AB .
83. A(6, 7), B(4, 3)
84. A(1, 5), B(2, 3)
85. If one line has a slope of -3 what must be the slope of (a.) any line parallel to it and (b.) any
line perpendicular to it?
86. If one line passes through the points (0,3) and (-4,1) what must be the slope of (a.) any line
parallel to that first line and (b.) any line perpendicular to that first line?
Statements
Reasons
⃗⃗⃗⃗
Given:
𝐺𝐽
𝑏𝑖𝑠𝑒𝑐𝑡𝑠
∠𝑂𝐺𝐻
⃗⃗⃗⃗ bisects OGH 1.
1. 𝐺𝐽
2.
2. Definition of an
angle bisector
̅̅̅
̅̅̅
3.
3. 𝐺𝐽 ≅ 𝐺𝐽
87.
Prove: ∆𝐺𝐽𝑂 ≅ ∆𝐺𝐽𝐻
88.
Prove: ∆𝑂𝑃𝑀 & ∆𝑂𝑁𝑀 are congruent
isosceles triangles

4. 𝑂𝐺 = ___________,
𝐻𝐺 = ___________
5. ̅̅̅̅
𝑂𝐺 ≅ ̅̅̅̅
𝐻𝐺
4. Distance Formula
6. GJO  GJH
6.
Given:
Reasonsof ∆𝑂𝑃𝑀 & ∆𝑂𝑁𝑀
Coordinates of the vertices
Statements
1. Coordinates of
1.
vertices of OPM
and ONM
2. OP = ______,
2. Distance Formula
PM = ______,

MN = ______,

NO = ______
3.
3. ̅̅̅̅
𝑂𝑃 ≅ ̅̅̅̅̅
𝑃𝑀 ≅
̅̅̅̅
̅̅̅̅̅ ≅ 𝑁𝑂
𝑀𝑁
̅̅̅̅̅
4.
4. 𝑂𝑀 ≅ ̅̅̅̅̅
𝑂𝑀
5.
5. OPM and 
ONM are isosceles
6. OPM  ONM 6.


5.


10
Triangle Coordinate Proofs: HOMEWORK – CP
For numbers 89 – 90 find (a.) the length of AB and (b.) the midpoint coordinates of AB .
89. A(14, 2), B(7, 8)
90. A(0, 0), B(5, 12)
91. If one line has a slope of 2/7 what must be the slope of (a.) any line parallel to it and (b.) any
line perpendicular to it?
92. If one line passes through the points (-2,5) and (7,-1) what must be the slope of (a.) any line
parallel to that first line and (b.) any line perpendicular to that first line?
93.
̅̅̅̅ 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝑇𝑂𝑅
Prove: 𝑂𝑆

Statements
̅̅̅̅
𝑂𝑆 ⊥ 𝑅𝑇
1. Given: ⃗⃗⃗⃗⃗
2. RSO and TSO
are right angles
3. RSO ≅ TSO
4. ̅̅̅̅
𝑂𝑆 ≅ ̅̅̅̅
𝑂𝑆
5. OR = 6, OT = 6
̅̅̅̅ ≅ 𝑂𝑇
̅̅̅̅
6. 𝑂𝑅
7. SOR  SOT
8. SOR  SOT
9. ⃗⃗⃗⃗⃗
𝑂𝑆 bisects TOR

94.
Prove: ∆𝐺𝐻𝐽 ≅ ∆𝐺𝐹𝑂
1.
3.
4.
5.
6.
7.
8.
9.
⃗⃗⃗⃗⃗
Given:
G is the midpoint Reasons
of 𝐻𝐹
Statements
1. Given
2.
G
Reasons
1. Given
2.
3. ̅̅̅̅
𝐻𝐺 ≅ ̅̅̅̅
𝐹𝐺
3. 𝑂𝐺 = ___________
𝐽𝐺 = __________
̅̅̅̅
5. 𝑂𝐺 ≅ ̅̅̅
𝐽𝐺
6. ∆𝐺𝐻𝐽 ≅ ∆𝐺𝐹𝑂
2. Vertical Angles
are 
3.
4. Distance Formula
5.
6.
11
Triangle Coordinate Proofs: CLASSWORK – Honors
For numbers 83 – 84 find (a.) the length of AB and (b.) the midpoint coordinates of AB .
83. A(6, 7), B(4, 3)
84. A(1, 5), B(2, 3)
85. If one line has a slope of -3 what must be the slope of (a.) any line parallel to it and (b.) any
line perpendicular to it?
86. If one line passes through the points (0,3) and (-4,1) what must be the slope of (a.) any line
parallel to that first line and (b.) any line perpendicular to that first line?
Given: ⃗⃗⃗⃗
𝐺𝐽 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝑂𝐺𝐻
87.
Prove: ∆𝐺𝐽𝑂 ≅ ∆𝐺𝐽𝐻
88.
Given: Coordinates of the vertices of
∆𝑂𝑃𝑀 & ∆𝑂𝑁𝑀
Prove: ∆𝑂𝑃𝑀 & ∆𝑂𝑁𝑀 are congruent isosceles triangles
12
Triangle Coordinate Proofs: HOMEWORK – Honors
For numbers 89 – 90 find (a.) the length of AB and (b.) the midpoint coordinates of AB .
89. A(14, 2), B(7, 8)
90. A(0, 0), B(5, 12)
91. If one line has a slope of 2/7 what must be the slope of (a.) any line parallel to it and (b.) any
line perpendicular to it?
92. If one line passes through the points (-2,5) and (7,-1) what must be the slope of (a.) any line
parallel to that first line and (b.) any line perpendicular to that first line?
93.
̅̅̅̅ 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝑇𝑂𝑅
Prove: 𝑂𝑆
̅̅̅̅
Given: ⃗⃗⃗⃗⃗
𝑂𝑆 ⊥ 𝑅𝑇
⃗⃗⃗⃗⃗
Given: G is the midpoint of 𝐻𝐹
94.
Prove: ∆𝐺𝐻𝐽 ≅ ∆𝐺𝐹𝑂
G
13
Equations of a Circle & Completing the Square: CLASSWORK
What are the center and the radius of the following circles?
95. (𝑥 + 2)2 + (𝑦 − 4)2 = 16
96. (𝑥 − 3)2 + (𝑦 − 7)2 = 25
97. (𝑥)2 + (𝑦 + 8)2 = 1
98. (𝑥 − 7)2 + (𝑦 + 1)2 = 17
99. (𝑥 + 6)2 + (𝑦)2 = 32
Write the standard form of the equation for the given information.
100. center (3,2) radius 6
101. center (-4, -7) radius 8
102. center (5, -9) radius 10
103. center (-8, 0) diameter 14
104. center (4,5) and point on the circle (3, -7)
105. diameter with endpoints (6, 4) and (10, -8)
106. center (4, 9) and tangent to the x-axis
PARCC-type Questions: Write the standard form of the equation for the given information.
107. 𝑥 2 + 4𝑥 + 𝑦 2 − 8𝑦 = 11
108. 𝑥 2 − 10𝑥 + 𝑦 2 + 2𝑦 = 11
109. 𝑥 2 + 7𝑥 + 𝑦 2 = 11
Are the following points on the circle (x-3)2+(y+4)2=25? Support your answer with your work.
110. (3,1)
111. (0,0)
112. (4,-1)
PARCC-type Question:
113. The equation 𝑥 2 + 𝑦 2 − 6𝑥 + 10𝑦 = 𝑏 describes a circle.
a. Determine the x-coordinate of the center of the circle.
b. Determine the y-coordinate of the center of the circle.
c. If the radius of the circle is 8 units, what is the value of b in the equation?
Equations of a Circle & Completing the Square: HOMEWORK
What are the center and the radius of the following circles?
114. (𝑥 − 9)2 + (𝑦 + 5)2 = 9
115. (𝑥 + 11)2 + (𝑦 − 8)2 = 64
116. (𝑥 + 13)2 + (𝑦 − 3)2 = 144
117. (𝑥 − 2)2 + (𝑦)2 = 19
118. (𝑥 − 6)2 + (𝑦 − 15)2 = 40
14
Write the standard form of the equation for the given information.
119. center (-2, -4) radius 9
120. center (-3, 3) radius 11
121. center (5, 8) radius 12
122. center (0 , 8) diameter 16
123. center (-4,6) and point on the circle (-2, -8)
124. diameter with endpoints (5, 14) and (11, -8)
125. center (4, 9) and tangent to the y-axis
PARCC-type Questions: Write the standard form of the equation for the given information.
126. 𝑥 2 − 2𝑥 + 𝑦 2 + 10𝑦 = 11
127. 𝑥 2 + 12𝑥 + 𝑦 2 + 20𝑦 = 11
128. 4𝑥 2 + 16𝑥 + 4𝑦 2 − 8𝑦 = 12
Are the following points on the circle (x-5)2+(y-12)2=169? Support your answer with your work.
129. (-4,2)
130. (0,0)
131. (-7,7)
PARCC-type Question:
132. The equation 𝑥 2 + 𝑦 2 + 12𝑥 − 4𝑦 = 𝑏 describes a circle.
a. Determine the x-coordinate of the center of the circle.
b. Determine the y-coordinate of the center of the circle.
c. If the radius of the circle is 5 units, what is the value of b in the equation?
15
Analytic Geometry Unit Review
Multiple Choice – Choose the correct answer for each question. No partial credit will be given.
1. What is the distance between points (-2, 1) and (2, 4)?
a. 3
b.
c. 5
d.
2.
What is the distance between points (1, 2) and (3, 4). Circle all that apply.
a. 2
b.
c. 2
d. 8
e. 2√5
f. 2√13
3.
What is the midpoint between points (-1, 4) and (7, 6)
a. (6, 5)
b. (3, 5)
c. (5, 5)
d. (5, 3)
4.
Find the midpoint between points (7, -9) and (3, 5)
a. (5, 2)
b. (2, 5)
c. (-5, 2)
d. (5, -2)
5.
The midpoint of a line segment is (3, 4). One endpoint has the coordinates (-3, -2). What
are the coordinates of the other endpoint?
a. (9, 10)
b. (-3, -2)
c. (10, 9)
d. (1, 0)
6. If one line passes through the points (7, -3) & (-2, 3), what must be the slope of a line parallel
to it?
3
a. − 2
2
b. − 3
c. 0
d. undefined
16
7. If one line passes through the points (-5, 3) & (9, 7) and a perpendicular line passes through
the point (-1, -3), what is another point that would lie on the 2nd line? Circle all that apply.
a. (-3, 4)
b. (-3, -11)
c. (6, -1)
d. (6, -5)
e. (-10, 1)
f. (1, 13)
8.
a.
b.
c.
d.
What is the equation of the line parallel to 2x + 8y = 10 and passes thru (-1, 5)?
y – 5 = - ¼(x – 1)
y – 5 = - ¼(x + 1)
y – 5 = 4(x – 1)
y – 5 = 4(x + 1)
9. What is the equation of the line perpendicular to y – 3 = 2/3(x + 3) and has an
x-intercept of 6?
a. y = 2/3x + 4
b. y = 2/3x – 4
c. y = -3/2x + 6
d. y = -3/2x + 9
10. What is the equation of the circle drawn in the figure
to the right?
a. (𝑥 − 6)2 + (𝑦 − 4)2 = 4
b. (𝑥 + 6)2 + (𝑦 + 4)2 = 6
c. (𝑥 − 6)2 + (𝑦 − 4)2 = 16
d. (𝑥 + 6)2 + (𝑦 + 4)2 = 36
Short Constructed Response – Write the correct answer for each question.
11. a) Write the distance formula and use it to find the distance between point B (-2, 5) to
point C (4, -3).
̅̅̅̅ ?
b) What are the coordinates of the midpoint of 𝐵𝐶
12. The equation of a circle is 𝑥 2 + 𝑦 2 − 8𝑥 − 6𝑦 = 75. Write the equation in standard
form.
17
13. Line segment AB in the coordinate plane has endpoints with coordinates A (-11, -6) and
B (11, 5).
a) Graph ̅̅̅̅
𝐴𝐵
b) Find 2 possible locations for
point C so that C divides ̅̅̅̅
𝐴𝐵
into 2 parts with lengths in a
ratio of 6:5.
Extended Constructed Response – Solve the problem, showing all work.
14. Draw the line m on the graph provided so that m passes thru (1, 4) and (5, -3)
a. What is the equation of the line?
b. Construct a parallel line n that contains (3, 7).
c. What is the equation of line n?
d. Construct a line p that is perpendicular to the original line that contains A(3, 7).
e. What is the equation of line p?
18
Statements
15. Given: The coordinates of
∆𝐺𝐻𝐽 & ∆𝐺𝐹𝑂
Prove: ∆𝐺𝐻𝐽 ≅ ∆𝐺𝐹𝑂
GGGG
(3,
Reasons
1.
1.
2.
2. Vertical Angles
are 
3. Slope formula
3. 𝑚𝐻𝐽 = ________
𝑚𝑂𝐹 = ________
̅̅̅̅ || ̅̅̅̅
4. 𝐻𝐽
𝑂𝐹
5. ∠𝐻 ≅ ∠𝐹
6. ______ is the
midpoint of ̅̅̅
𝐽𝑂
̅̅̅̅ ≅ 𝐽𝐺
̅̅̅
7. 𝑂𝐺
8. ∆𝐺𝐻𝐽 ≅ ∆𝐺𝐹𝑂
4.
5.
6. Midpoint formula
7.
8.
16. The points (3, 2) and (9, 12) are the endpoints of a diameter of a circle.
a. Where is the center of the circle?
b. How long is the diameter of the circle?
c. Write the equation of the circle?
d. Is the point (5, 6) inside, on, or outside the circle? Justify your answer.
17. The equation 𝑥 2 + 𝑦 2 − 8𝑥 + 6𝑦 = 𝑏 describes a circle.
a. Determine the x-coordinate of the center of the circle.
b. Determine the y-coordinate of the center of the circle.
c. If the radius of the circle is 10 units, what is the value of b in the equation?
19
Answers: CW/HW problems:
1. 5
31. See graph below for a) & b)
2. 3 13 ≈ 10.82
34 √34 ≈ 5.83
3.
4. 13
5. 3 2 ≈ 4.24
6. 5 2 ≈ 7.07
7. 13
8.
53 ≈ 7.28
9.
26 ≈ 5.10
10. 10 ≈ 3.16
11. (3, 5)
12. (4, 5)
13. (1, 2)
14. (5, 1)
15. (-1.5, -10)
16. (4.5, 4)
17. (-2.5, 3)
18. (10, 16)
19. (-4, -4)
20. (1, 10)
21. (4, 2)
22. (3, 1)
23. (5, -2)
24. (4, 3.5)
25. (-4, -4)
26. (3.5, 1)
27. (-1.5, 0.5)
28. (-11, -13)
29. (14, -21)
30. (-4, 10)
32. See graph below for a) & b)
33. (-1, -1) & (2, 2)
34. (2, -4) & (-8, 6)
35. (-3, 4) & (1, -2)
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36. See graph below for a) & b)
37. See graph below for a) & b)
38. (-4, -4) & (5, 5)
39. (-4, 2) & (-2, 0)
40. (-7, 10) & (5, -8)
41. 3
42. No slope (undefined)
43. 0
44. a. no; slope of j=2, slope of k = 4/3;
b. yes; slope of j and k = -4/5
45. a. yes; slope of j= -1/6; slope of k=6;
b. no slope of j= -1; slope of k= 1/3
46. m = -5
47. ½
48. Multiple Answers: Sample points
that work include (4, -3) & (2, 11)
49. -2
50. 1/7
51. Multiple Answers: Sample points
that work include (1, 5) & (5, 3)
52. -7/4
53. 0
54. No slope (Undefined)
55. a. yes; slope of j & k = 4/7;
b. no; slope of j= -1/6, slope of k= -1/7
56. a. no slope of j= 3/2; slope of k=-1/2;
b. yes, slope of j=1/5; slope of k= -5
57. ½
58. -7
59. Multiple answers: Sample points that
work include (2, 2) & (0, -2)
60. m = 1/5
61. -2
62. Multiple Answers: Sample points
that work include (-4, 3) or (10, 5)
63. y -5= 2(x+2)
64. k= -1/2
65. y= -3/4x+3
66. Yes,𝑦 = 4𝑥 + 5䚫8𝑥 − 2𝑦 =
1
1 ; 𝑦 = 3 𝑥 + 7䚫𝑥 − 3𝑦 = 2
67. y=-2x+3
68. k= -2
69. y=-1/4x
70. no, y=4x +5 and y =1/3x +7 are not
perpendicular
71. perpendicular
72. neither
73. y -2 = 3(x+3)
74. k=1/3
75. y-3=-3/4(x+8)
76. no;
77. y=3/2x+11
78. k=-3/2
79. y=1/2x-6
80. yes, slopes are m=-1/4 and 4
81. parallel
82. neither
83. a.) 2√5 or 4.5 b.) (5, 5)
84. a.) √73 or 8.5 b.) (0.5, 1)
85. a.) -3 b.) -1/3
21
86. a.) ½ b.) -2
87.
Statements
⃗⃗⃗⃗ bisects OGH
1. 𝐺𝐽
2. OGJ  HGJ
3. ̅̅̅
𝐺𝐽 ≅ ̅̅̅
𝐺𝐽
4. 𝑂𝐺 = √34,
𝐻𝐺 = √34
5. ̅̅̅̅
𝑂𝐺 ≅ ̅̅̅̅
𝐻𝐺
6. GJO  GJH
̅̅̅̅ ≅ 𝑂𝑇
̅̅̅̅
6. 𝑂𝑅
Reasons
1. Given
2. Definition of an
angle bisector

3. Reflexive Prop. of

4. Distance Formula
5. Def. of 
segments
6. SAS Postulate

Statements
1. Coordinates of
vertices of OPM
and ONM
2. OP = 5, PM = 5,
MN = 5, NO = 5

3. ̅̅̅̅
𝑂𝑃 ≅ ̅̅̅̅̅
𝑃𝑀 ≅

̅̅̅̅
̅̅̅̅̅
𝑀𝑁 ≅ 𝑁𝑂
̅̅̅̅̅ ≅ 𝑂𝑀
̅̅̅̅̅
4. 𝑂𝑀
5. OPM and 
ONM are isosceles
6. OPM  ONM


Reasons
1. Given
6. GHJ  GFO
2. Distance Formula
3. Def. of 
segments
4. Reflexive Prop. of

5. Definition of an
isosceles triangle
6. SSS Postulate

89. a.) √85 or 9.2 b.) (10.5, -5)
90. a.) 13 b.) (-2.5, 6)

91. a.) 2/7
b.) -7/2
92. a.) -2/3 b.) 3/2
93.
Statements
Reasons
̅̅̅̅ ⊥ 𝑅𝑇
̅̅̅̅
1. Given
1. 𝑂𝑆
2. RSO and TSO 2. Definition of ⊥
lines
are right angles
3. All right angles
3. RSO ≅ TSO
are congruent
̅̅̅̅
̅̅̅̅
4. Reflexive Prop. of
4. 𝑂𝑆 ≅ 𝑂𝑆

5. OR = 6, OT = 6
5. Given in diagram;
or Distance formua
94.
Statements
1. G is the midpoint
̅̅̅̅
of 𝐻𝐹
2. HGJ  FGO
̅̅̅̅ ≅ 𝐹𝐺
̅̅̅̅
3. 𝐻𝐺
4. 𝑂𝐺 = 3√2
𝐽𝐺 = 3√2
̅̅̅̅
5. 𝑂𝐺 ≅ ̅̅̅
𝐽𝐺
88.

7. SOR  SOT
8. SOR  SOT
9. ⃗⃗⃗⃗⃗
𝑂𝑆 bisects TOR


6. Def. of 
segments
7. HL Theorem
8. CPCTC
9. Definition of an
angle bisector
Reasons
1. Given
2. Vertical Angles
are 
3. Def. of midpoint
4. Distance Formula
5. Definition of 
segments
6. SAS Postulate
95. C(-2,4); r=4
96. C (3,7); r=5
97. C (),-8); r=1
98. C (7,-1); r= √17
99. C (-6,0); r =4√2
100.
(x-3)2 + (x-2)2 =36
101.
(x+4)2 + (Y+7)2 =64
102.
(x-5)2 + (y+9)2 = 100
103.
(x+8)2 + y2 =49
104.
(x-4)2 + (y-5)2 =145
105.
(x-8)2 + (y+2)2 =40
106.
(x-4)2 + (y-9)2 =81
107.
(x+2)2 + (y-4)2 =31
108.
(x-5)2 + (y+1)2 =37
109.
(x+3.5)2 + y2 =23.25
110.
yes; (3-3)2+(1+4)2=25
111.
yes; (0-3)2+(0+4)2=25
112.
no; (4-3)2+(-1+4)2=10
113.
a) x-coord. = 3
b) y-coord. = -5
c) b = 30
114.
C (9,-5) r=3
22
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
C -11, 8) r=8
C(-13, 3) r=12
C(2,0) r= √19
C (6,15) r=2√10
(x+2)2 +(Y+4)2 =81
(x+3)2 + (y-3)2 =121
(x-5)2 + (y-8)2 =144
x2 + (y-8)2 =64
(x+4)2 + (y-6)2 =200
(x-8)2 + (y-3)2 = 130
125.
126.
127.
128.
129.
130.
131.
132.
(x-4)2 + ( y-9)2 =130
(x-1)2 + (y+5)2 =37
(x+6)2 + (y+10)2 =147
(x+2)2 + (y-1)2 =8
no; (-4-5)2+(2-12)2=181
yes; (0-5)2+(0-12)2=169
yes; (-7-5)2+(7-12)2=169
a) x-coord. = -6
b) y-coord. = 2
c) b = -15
Answers: Unit Review
Multiple Choice
1.
C
2.
B&C
3.
B
4.
D
5.
A
6.
B
7.
A&E
8.
B
9.
D
10. C
Extended Constructed Response
14. a. y – 4 = -7/4(x – 1)
or y + 3 = -7/4(x – 5)
b. construct 𝑦 − 7 = −7/4(𝑥 − 3)
in coordinate plane
c. y – 7 = -7/4(x – 3) or
y = -7/4x + 49/4 or
7x + 4y = 49
d. construct 𝑦 − 7 = 4/7(𝑥 − 3)
in coordinate plane
e. 𝑦 − 7 = 4/7(𝑥 − 3) or
y = 4/7x + 37/7 or
4x – 7y = -37
15.
Statements
Reasons
1. The coordinates of 1. Given
∆𝐺𝐻𝐽 & ∆𝐺𝐹𝑂
2. Vertical Angles
2. HGJ  FGO
are 
3. Slope formula, or
3. 𝑚𝐻𝐽 = 0
Horizontal lines
𝑚𝑂𝐹 = 0
have a slope of 0.
̅̅̅̅
̅
̅
̅
̅
4. Def. of || lines
4. 𝐻𝐽 || 𝑂𝐹
5. ∠𝐻 ≅ ∠𝐹
5. Alt. Int. ∠𝑠 ≅
6. G is the midpoint 6. Midpoint formula
of ̅̅̅
𝐽𝑂
̅̅̅̅ ≅ 𝐽𝐺
̅̅̅
7. Definition of
7. 𝑂𝐺
midpoint
8. GHJ  GFO
8. AAS Theorem
Short Constructed Response
11. d = 10; midpoint = (1, 1)
12. (𝑥 − 4)2 + (𝑦 − 3)2 = 100
13. See graph below for a) & b)


23
16. a. (6,7)
b. 11.662
c. (𝑥 − 6)2 +(𝑦 − 7)2 = 136
d. (5 − 6)2 +(6 − 7)2 = 2
2 < 136, so the point is inside the
circle.
17. Equation:
(𝑥 − 4)2 + (𝑦 + 3)2 = 𝑏 + 25
a. 4
b. -3
c. b = 75, since 𝑟 2 = 100
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