# Worksheet: Slopes of Parallel and Perpendicular Lines

In this worksheet, we will practice using the concept of slopes to determine whether two lines are parallel or perpendicular and using these geometric relationships to solve problems.

Q1:

Two lines are perpendicular. What will the product of their slopes be?

Q2:

If the line passing through points and is parallel to the line passing through points and , what is the value of ?

Q3:

Two lines and have slopes of and respectively. Are the two lines perpendicular?

• AYes
• BNo

Q4:

Two lines and have slopes of and respectively. Are the two lines parallel or perpendicular?

• AParallel
• BPerpendicular

Q5:

Which of the following relates the slopes and of two parallel lines?

• A
• B
• C
• D

Q6:

If and the slope of , find the slope of .

• A
• B
• C
• D

Q7:

Find the gradient of the straight line which is parallel to the straight line passing through the points and .

• A
• B
• C
• D
• E7

Q8:

If and the slope of , find the slope of .

• A
• B
• C
• D7

Q9:

If the two straight lines whose slopes are and are perpendicular, what is the value of ?

Q10:

Suppose that the points , and are such that . What is the value of ?

Q11:

Which of the following relates the slopes and of two perpendicular lines?

• A
• B
• C
• D

Q12:

Let be the line on points and . What is the slope of the perpendicular to that passes through the origin ?

• A
• B
• C
• D

Q13:

Given that is a trapezoid, where , and the coordinates of points , , , and are , , , and , respectively, find the coordinates of point .

• A
• B
• C
• D

Q14:

The coordinates of points , , , and are , and respectively. Are the line segments and perpendicular?

• AYes
• BIt is impossible to tell.
• CNo

Q15:

Complete the following definition. Two line segments are said to be perpendicular if the product of their slopes is .

Q16:

The slope of the straight line that is parallel to the -axis is .

Q17:

Lines and are perpendicular to each other and meet at . If the slope of is 0, what is the equation of line ?

• A
• B
• C
• D
• E

Q18:

What is the value of , if lines and are parallel?

• A
• B
• C
• D

Q19:

Two lines have slopes of and , and cut the -axis at different points. Are the two lines parallel?

• ANo
• BYes

Q20:

The line passes through the points and , and the line passes through the points and . Are the two lines perpendicular?

• Ano
• Byes

Q21:

Let be the line through the points and and the line through and . Which of the following is true about the lines and ?

• AThey are intersecting but not perpendicular .
• BThey are parallel.
• CThey are perpendicular.

Q22:

If the line that passes through the points and is perpendicular to the line passing through the points and , what is the value of ?

Q23:

The line on the points and is parallel to one that makes an angle of with the positive -axis. Determine to the nearest integer.

• A9
• B11
• C
• D7

Q24:

Two lines and have slopes of and respectively. Are the two lines perpendicular?

• AYes
• BNo

Q25:

The line through points and is perpendicular to the line . Find .