3.5 Equations of Parallel and Perpendicular Lines

3.5 Equations of Parallel and Perpendicular Lines

by Mary Lett

​Objective and Standards

• ​HSG-CO.C.9: Prove theorems about lines and angles

• ​HSG-CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, ...)

• Students will be able to calculate the distance from a point to a line and find the equations of parallel and perpendicular lines.

​Distance from a point to a line

​Example of Distance from a point to a line

​Example of Distance from a point to a line

Multiple Choice

What is the shortest distance between a point and a line?

• The length of the perpendicular segment from the point to the line.

• The length of the parallel segment from the point to the line.

• The circumference of the semi-circle from the point to the line.

• None of the above.

Fill in the Blank

Find the distance between y= x + 3 and y= x -3. ( round to the nearest tenth when the answer isn't an integer)

​Parallel Lines

​Perpendicular Lines

Multiple Choice

Two lines that are parallel will have ...

• Slope that is opposite reciprocals

• No slope

• Slope that is the same

• none of the above

Multiple Choice

Two lines that are perpendicular lines have ...

• Slope that is opposite reciprocals

• No Slope

• Slope that is the same

• none of the above

Multiple Choice

What slope is perpendicular to:  
m = 5/8

• -5/8
• 5/8
• -8/5
• 8/5

Multiple Choice

What slope is parallel to:  
m = 4

• 4
• -1/4
• -4
• 1/4

Multiple Choice

y = 6x + 2
y = -6x + 2
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

y = -2/3x + 2
y = 3/2x + 9
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

A line is parallel to   y = 2x - 7.
What is it's slope?

• -2
• 1/2
• -1/2
• 2

Multiple Choice

Which is the equation of the line that is parallel to the graph of y = 5x + 7 and has a y-intercept at (0, -2)?

• y = 5x - 2

• y = -2x + 7

• y = 5(x - 2)

• y = -1/5x - 2