Name _________________________________________
Period ____
9/26 – 10/11
GEOMETRY UNIT 3 – COORDINATE GEOMETRY
Vocabulary Terms:
Bisector
Midpoint
Slope
Rate of Change
Coordinate Plane
Y axis
X axis
Vertical
10/1
Mixed Practice
10/8
INSERVICE
Horizontal
Diagonal
Coordinate
Ratio
Distance
Length
Pythagorean
Theorem
Square Root
Oblique
Legs
Point-slope form
Hypotenuse
Standard form
Parallel
Coincide
∆y
Perpendicular
∆x
Reciprocal
rise
Slope-Intercept form
run
y-intercept
9/26-27
9/28
Slope and Midpoints
Distance
10/2
10/3-4
10/5
Graphing
Perpendicular Bisectors
Coordinate Proofs
(End
of 6 weeks) – Eligibility Check
Parallel or Perpendicular
Writing Equations
10/9
10/10-11
Review
Test #3
Wednesday or Thursday, 9/26-27
Chapter 1 Section 6: Midpoint and Distance and Chapter 3 Section 5: Slopes
I can find the slope given points, graphs, or equations.
I can solve problems involving the midpoint on a coordinate plane.
Activity – Slope Investigation on iPad Sketch Explorer
ASSIGNMENT: Slope and Midpoint Worksheet
Completed:
Friday, 9/28
Chapter 1 Section 6: Midpoint and Distance
I can find the distance between points on a coordinate plane.
ASSIGNMENT: Distance Worksheet
Completed:
Monday, 10/1
Chapter 1 Section 6: Midpoint and Distance and Chapter 3 Section 5: Slopes
I can find the distance between points on a coordinate plane.
I can solve problems involving the midpoint on a coordinate plane.
I can find the slope given points, graphs, or equations.
ASSIGNMENT: pg. 47 (#21, 23-25, 28-30, 32, 36, 40) 10 problems
Completed:
Tuesday, 10/2
Chapter 3 Section 5: Slopes of Lines
I can determine if lines are parallel, perpendicular, coninciding, or oblique.
I can make valid conjectures given information in various forms.
ASSIGNMENT: Pg. 185 (#7 – 9, 15 – 17, 26, 31) 8 problems
Completed:
Wednesday or Thursday, 10/3-4
Chapter 3 Section 6: Lines in the Coordinate Plane
I can use the coordinate plane to represent geometric figures.
I can find the perpendicular bisector of a segment on the coordinate plane.
I can transform equations of lines between the different forms.
ASSIGNMENT: Pg. 194 (#1-4, 8-11, 32-38, 47-49) 18 problems
Completed:
Friday, 10/5
Chapter 4 Section 7: Coordinate Proofs
I can use the coordinate plane to represent geometric figures.
I can use logical reasoning to prove statements are true or find a counter example to prove them false.
I can provide and recognize a valid deductive argument.
ASSIGNMENT: Pg. 271 (#4, 120 , 13, 21, 27, 30) 6 problems
Completed:
Tuesday, 10/9
Review Day
Completed:
ASSIGNMENT: Review for Test
sday or Thursday, 10/10-11
Test Day
Unit 3Test: Coordinate Geometry
Grade:
If you miss the review day, you are still expected to take the test on the test day.
For more help BEFORE the test:
1. Use the indicated chapters in your book
2. Use the book online (it has videos and a homework help section)
3. Use Google to find more resources
4. Come to tutoring (with assignment)
We
dne
Write the slope formula - ___________
Slope Examples
Always label your points!!
Ex 1 – Find the slope using the following points A(-3, 1) and B(9, -5).
Ex 2 – Examine the graph below and determine the slope.
Ex 3 – Determine the slope from the given equation.
7
What else can we call the slope of an equation?
Midpoint Examples
Midpoint Formula:
1. Find the midpoint of MS if M ( −4,10 ) and S (12,8 )
Method 1
Method 2
2.Find the midpoint of AC if A ( −2, 3) and C ( 5, −3) .
1. Why are formulas
necessary?
2. How are different
methods of finding
locations useful?
Choose your own method.
3. If the midpoint is (7, 5) and one endpoint is (5, -6), what is the other endpoint?
Method 1
Method 2
4. If the midpoint for a segment is ( −6, −1) and one endpoint is ( −1,1) , which would be the other endpoint?
Choose your own method.
What other special
slope do we have?
What does it look
like?
Slope and Midpoint Practice:
Identify the slope from the different methods.
1.
2.
4. y =
3
x+4
2
3.
5. y = x -2
8. A is (2,18) and B is (-16,9)
6. y =
−3
x
4
7. 7 1
9. A is (5,-8) and B is (19, -4)
10. A is (-10, -1) and B is (-14, 13)
11. A is (10,-6) and B is (8,6)
Find the midpoint of each segment AB below.
12. A is (-3,1) and B is (9,-5)
13. A is (5,-8) and B is (19, -4)
14. A is (2,18) and B is (-16,9)
Let M be the midpoint of segment AB. Find the other end point if
15. M is (-10, -1) and A is (-14, 13)
16. A is (-4, 6) and M is (3, -8)
17. M is (10,-6) and B is (8,6)
18. Sue’s work for finding midpoint is shown below. Please check it for mistakes. If he made one, fix it.
Find the midpoint for the points ( −3, −7 ) and ( −1,1)
 −3 + −7 −1 + 1 
,


2 
 2
 −10 0 
, 

 2 2
( −5, 0 )
Distance Examples
Leave your answer in decimal form.
1. Find the length of BE if B ( −3, 3 ) and E ( −15,17 )
Distance Formula:
How do we get this formula?
2. Find the length of GO if G ( −1,1) and O ( − 3, −4 ) .
Distance Practice
Leave your answer in decimal form.
Find AB if:
1. A is (4,0) and B is (-12,4)
2.A is (-3,1) and B is (9,-5)
3. A is (-7,3) and B is (5, -3)
4. A is (2,-2) and B is (8,4)
5. Jose’s work for finding distance is shown below. Please check it for mistakes. If she made one, fix it.
Find the length of AT if A ( −2, 3 ) and T ( 2, −2 )
2
d=
( 2 + 9 ) + ( −2 − 3)
d=
(11) + ( −5)
2
2
2
d = 121 − 25
d = 96
d ≈ 9.80
CHALLENGE. Given endpoint C (1, 2) ,which other endpoint would create a segment with length of 5.
A. ( 5, 5 )
B. ( 2, 2 )
C. ( −5, −5 )
D. ( −2, −2 )
Parallel or Perpendicular Day
Objectives:
1. Student will be able to determine parallel, perpendicular, coinciding, or oblique from points, equations, or
graphs.
2. Students will be able to graph points and lines.
Warm – up:
Please graph the following:
1) A(3, -5) and B (-4, 0)
2) y = 2x – 5
Reminders about graphing:
Vocabulary:
Parallel: 2 coplanar lines that do not ever touch
Perpendicular: 2 coplanar lines that intersect at a right angle
Oblique: 2 coplanar lines that intersect, but not at a right angle
Coincide: 2 lines that overlap each other exactly
Notes and Examples:
•
If lines are parallel, then their slopes are ________________________________.
•
If lines are perpendicular, then their slopes are ___________________________________________.
•
A ____________________ or ___________________ reciprocal is when you __________________ the signs
and ______________________ the numerator and denominator. Their products will always be _________.
•
_____________ is when two lines cross, but are not perpendicular.
•
______________ is when the lines are the exact same line.
For each set of lines determine if they are parallel, perpendicular, coinciding, or oblique.
1) y =
2
2
x + 5 and y = − x + 1
7
7
3) 4 x + y = 9 and y = 9 − 4 x
5) y = −3 x − 3 and y =
2) y =
5
5
x − 3 and y = x + 7
2
2
4) AB where A(3, 4) and B(-3, 2) and CD where C(3, -9) and D(0, 0)
1
x+7
3
MC Questions
1. What would a line that is perpendicular to the line RS would have regarding slope and yintercept?
a.
b.
c.
d.
positive slope, positive y-intercept
positive slope, negative y-intercept
negative slope, positive y-intercept
negative slope, negative y-intercept
2. Determine the relationship between the lines 6x + 9y = 3 and 2x + 3y = 1.
a) The lines are parallel.
b) The lines are perpendicular.
c) The lines coincide.
d) The lines intersect, but are not perpendicular.
Practice: Pg. 185 (#7 – 9, 15 – 17, 26, 31)
Notes – Point Slope Form
Point-Slope Form of a Linear Equation (found on a formula chart): ______________________________________
Write an equation of a line given a slope and a point. Then, re-write the equation in slope-intercept form.
Ex: Slope = 3 Point = (1, 1)
Your Turn: Slope = −
1
Point = (3, -2)
2
Write an equation of a line parallel to the given line and through the given point.
Ex: y =
3
x + 4 Point = (2, 6)
2
Your Turn: y = −4 x + 7 Point = (4, 2)
Write an equation of a line perpendicular to the given line and through the given point.
Ex: y =
−1
1
x − 9 Point = ( , 1)
4
2
Your Turn: y = −5 x + 1 Point = (10, 1)
Perpendicular Bisectors:
A perpendicular bisector is a _________________ perpendicular to a segment at the segments ____________________.
Sketch a picture with the correct markings to show a perpendicular bisector.
Construct a perpendicular bisector.
http://www.mathopenref.com/tocs/constructionstoc.html
Write the equation of the perpendicular bisector to the line through the given points.
1.
(0, -2) and (4, 6)
2. (2, 0) and (0, 4)
STEPS:
Name _____________________________________________ Period _____________
Review Unit 3 – Coordinate Lines and Segments
For 1-2, find the slope, distance, and midpoint between the following points.
1. (7, 6) ( -1, -2)
2. (5, 1) (-3, 7)
3. Given PQ with midpoint L. Find the missing point if P(5, -1) and L(-2, 4)
For 4-5, find the equation of the perpendicular bisector between the following sets of points.
4. (-3, 4) (1, -2)
5. (7, 6) (5, 10)
For 6-7, write the equation of the line through the two points in point-slope form, slope intercept form, and standard
form.
6. (-2, 2) (2, -1)
7. (-2, -2) (4, 1)
Write the equation of the line both parallel to and perpendicular to the lines with the following conditions.
8. Line from # 6 through (7, -3)
9. Line from #7, through (-5, 6)
10.Write the equation of a vertical line through ( -3, 0)
11.Write the equation of a horizontal line through(0,4)
12. Given the following list of equations, list all groups of parallel lines and all pairs of perpendicular lines.
Parallel lines have ____________________________
Parallel Groups:
A.
E.
B.
F.
Perpendicular Lines have __________________________
Perpendicular Groups:
C.
G.
D.
Use the slopes to determine if the lines are parallel, perpendicular, or neither.
H.
13. A(1, 0) B(5, 3) and C(6, -1) D(0, 2); slope of AB _____ slope of CD ______
Circle one: parallel
perpendicular neither
14. A(5, 1) B(-1, -1) and C(2, 1) D(3, -2) slope of AB _____ slope of CD ______
Circle one: parallel
perpendicular neither
For 15 – 17, given the following graphs, determine if each pair of lines is parallel, perpendicular, or oblique.
15.
16.
17.
For 18-19, given the following sets of 3 points, classify the triangle formed.
18. A(-1, -1) B (3, 1) C(5, -3)
19. A(-4, 1) B(-2, -1) C(4, 3)