Aim #6: How do we identify and write equations of parallel and perpendicular lines?

Do Now:1) If two lines are perpendicular, their slopes are _________ __________.2) If two lines are perpendicular, the product of their slopes is ______.

CC Geometry H

3) Which line(s) are perpendicular to the line with equation 2y - 3x = 0?

(a) 6y = -4x (b) y + + 1 = 0 (c) 6x = 8 - 9y (d) y =

4) Write a conclusion: If line x line r and line y line r, then ________________

If two lines are parallel, their slopes are _________.

Which line(s) are parallel to the line with equation 2y - 3x - 10 = 0?

(a) 3x - 2y = 8 (b) 12x + 8y = 0

(c) 4y = 6x (d) ½y = ¾x - 2

45

3) Two lines having the same y-intercept are perpendicular. If the equation of one of these lines is y = - x + 6, what is the equation of the second line?

Exercises32

1) Determine whether the lines given by the equations 2x + 3y = 6 and y = x + 4 are perpendicular. Justify your answer.

2) Given a point (-3,6) and a line y = 2x – 8.a. Write an equation of a line through the given point and parallel to the given

line in point-slope form.

b. What is the slope of any line perpendicular to the given line? _______

4) a. Find an equation of a line through (0,-7) and parallel to the line y = x + 5.

b. If a line is perpendicular to y = x + 5, will it be perpendicular to x – 2y = 14?

12

12

5) Write an equation of the line that passes through the origin which intersects the line 2x + 5y = 7 to form a right angle.

6) Find an equation of a line through ( , .5) parallel to the line

a. x = – 9 b. y =

c. What can you conclude about the lines in your answers to parts (a) and (b)?

7) Find an equation of a line through that is parallel to the line x – 7y = .

8) a. If the line y = 2x - 3 is dilated by a scale factor of 2, centered at the origin, write an equation that represents the image of the line after the dilation.

b. If a line is dilated, what happens to the slope? Explain your answer.

9) Line y = -3x - 5 is transformed by a dilation with a scale factor of 2 and centered at (-3,4). Write an equation that represents the image of the line.

10) A robot, moving at a constant speed of 2 feet per second, starts at position (20, 50) on the coordinate plane, and heads in a southeast direction along the line 3x + 4y = 260. After 15 seconds, it turns clockwise 90° and travels in a straight line in this new direction.

(20,50)

b. Find an equation for the second line on which the robot traveled.

c. If, after turning, the robot travels for 20 seconds along this line and then stops, how far will it be from its starting position?

d. What is the equation of the line the robot needs to travel along in order to now return to its starting position? How long will it take for the robot to get there?

a. What are the coordinates of the point at which the robot made the turn? To help you: -How many feet does the robot travel before it turns? -How does the slope help you find the total vertical and horizontal distances traveled by the robot before the turn?

1) Are the pairs of lines parallel, perpendicular, or neither? Justify your answer.

a. 3x + 2y = 74 and 9x – 6y = 15 b. 4x – 9y = 8 and 18x + 8y = 7

3) Write the equation of the line through (-5,3) that is:

a. parallel to x = -1 b. perpendicular to x = -1

c. parallel to y = x + 2. d. perpendicular to y = x + 2 35

35

4) Write the equation of the line through ( , ) and:

a. parallel to y = 7 b. perpendicular to y = 7

34

12

34c. perpendicular to x – y = 10

2) Write the equation of the line passing through (–3, 4) and perpendicular to 2x + 7y = –3 in point-slope form.

5) Find an equation of a line through parallel to the line x – 7y = .

CC Geometry H HW #6

Name ______________________ Date ______________________

7) Given the statement "AB is parallel to DE", construct an argument for or against this statement using the two triangles shown.

Review

6) The line y = 3x - 4 is dilated by a scale factor of 2, centered at the origin. Which equation represents the image of the line after the dilation?

a) y = 6x - 8 b) 2y = 6x - 8 c) y = 6x - 4 d) y = 3x - 8

Given: AD bisects BC at E. AB BC and DC BC. Prove: AB ≅ DC.

8) Given AB shown, what is an equation of theline that passes through the point P and is parallel to AB?

A

B

P

A

BC

D

E