Honors Geometry 1. Homework Answers for Section 13.2 Find the slope and the y-intercept of the graph of each equation.
a. y = 3x + 7
3; 7
b. y = 4x
4; 0
c. y =
1
2
x- 3
1
2
;- 3
d. y = 13 - 6x
-6; 13
e. y = -5x - 6
-5; -6
f. y = 7
0; 7
2. Rewrite each equation in y-form and find the slope and the y-intercept of its graph.
a. y - 3x = 1
y = 3x + 1; 3; 1
b. y + 5x = 2
y = -5x = 2; -5; 2
c. 2x + 3y = 6
y=-
d. 7 - (6 - 2x) = 4y
y=
2
2
x + 2; - ; 2
3
3
1
1 1 1
x+ ; ;
2
4 2 4
3. Write an equation of a line that is 6 units below, and parallel to , the x-axis.
y = -6
4. Write an equation of a line that is perpendicular to the x-axis and passes through (8, 1).
x=8
5. Which two of the following three lines are parallel?
a. y = 5x - 1
b. y = 7x + 2
c. y = 2 + 5x
Baroody a & c are parallel...they both have a slope of 5.
Page 1 of 5 Honors Geometry 6. Homework Answers for Section 13.2 Write the y-form equation of each line.
a. y-intercept of 2; slope = 4.
y = 4x + 2
b. m = 5; passes through (0, -2).
y = 5x - 2
c. Parallel to graph of y = 10x - 6; y-intercept of 1.
y = 10x +1
d. Perpendicular to graph of 2y = x + 16; passes through (0, -5).
y = -2x - 5
e. y-intercept of 2; perpendicular to line containing (-4, 6) and (1, 11).
y = -x + 2
10. CD is ⊥ to the graph of 2x + 3y = 8. If C = (1, 4), find the equation of CD.
2x + 3y = 8
y = mx + b
3y = -2x + 8
y=-
2
8
x+
3
3
∴ slope of CD is
4=
3
(1) + b
2
b=
8 3
5
=
2 2
2
3
2
∴ The equation of CD is y =
Baroody 3
5
x+
2
2
Page 2 of 5 Honors Geometry 14. Homework Answers for Section 13.2 Write an equation of the perpendicular bisector of AB.
m of AB =
3-1
16 - 2
=
2
14
m of ⊥ bisector is -
=
1
midpoint of AB =
7
7
or -7
1
(
16 + 2
2
,
3+1
2
)
= (9, 2)
y = mx + b
2 = -7(9) + b
y-axis
b = 2 + 63 = 65
C (4, 12)
∴ The equation of ⊥ bis is y = -7x + 65
B (16, 3)
A (2, 1)
x-axis
15. Write an equation of the altitude from C to AB.
m of AB =
3-1
2
1
=
=
16 - 2
14
7
m of altitude is -
y = mx + b
12 = -7(4) + b
7
or -7
1
b = 12 + 28 = 40
y-axis
C (4, 12)
∴ The equation of the altitude is
y = -7x + 40
B (16, 3)
A (2, 1)
Baroody x-axis
Page 3 of 5 Honors Geometry 16. Homework Answers for Section 13.2 Write an equation of the median from C to AB.
midpoint of AB =
(
16 + 2
2
,
3+1
2
)
= (9, 2)
m of CM =
12 - 2
4-9
=-
10
5
= -2
y = mx + b
2 = -2(9) + b
y-axis
b = 2 + 18 = 20
C (4, 12)
∴ The equation of the median is y = -2x + 20
B (16, 3)
A (2, 1)
M
x-axis
17. Find the slope of the line passing through the midpoints of AC and BC.
midpoint of AC =
midpoint of BC =
(
(
) ( )
) ( )
2 + 4 12 + 1
13
,
= 3,
2
2
2
16 + 4 3 + 12
15
,
= 10,
2
2
2
13 15
2
2
2
2
1
m is =
=
=
3 - 10
-7
7
y-axis
C (4, 12)
B (16, 3)
A (2, 1)
Baroody x-axis
Page 4 of 5 Honors Geometry 19. Homework Answers for Section 13.2 If P = (-2, 5) and R = (0, 9), write, in point-slope form, an equation of the perpendicular bisector of PR.
The midpoint of PR is
(
The slope of PR is m =
-2 + 0
2
,
9-5
0 - (-2)
5+9
2
=
)
= (-1, 7)
4
1
= 2. ∴ the slope of the ⊥ bisector is - .
2
2
Since (-1,7) is on the line, point-slope form would be:
y-7=-
1
1
(x - (-1)) or y - 7 = - (x + 1)
2
2
25. Find the center of the circle containing D = (-3, 5), E = (3, 3), and F = (11, 19). Note that the center of
this circle is called the circumcenter of DEF.
The center can be found by finding the point of intersection
of the perpendicular bisectors of two chords of the circle.
F (11, 19)
C (3, 13)
(
)
3 + (-3) 3 + 5
,
= (0, 4)
2
2
3-5
2
1
and the slope of DE is
=- =- .
3 - (-3)
6
3
∴ the equation of the ⊥ bisector of DE is y = 3x +4
The midpoint of chord DE is
Similarly, the equation of the ⊥ bisector of EF is
1
29
y=- x+
.
2
2
Solving these simultaneously shows:
1
29
3x + 4 = - x +
2
2
D (-3, 5)
E (3, 3)
6x + 8 = -x + 29
7x = 21
x = 3; y = 13
Baroody Page 5 of 5