# Lesson Worksheet: Slopes of Parallel and Perpendicular Lines Mathematics • 11th Grade

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:

If the angle that a straight line makes with the positive when measured counterclockwise is , what will the slope of the straight line be?

• ANegative
• BUndefined
• CPositive
• DZero

Q2:

Find, to the nearest two decimal places, the slope of the line that makes a positive angle of with the positive direction of the .

Q3:

Consider a line with slope 1 and another line that makes an angle of with the in a counterclockwise direction. Which of the following is correct about the two lines?

• AThe two lines are perpendicular.
• BThe two lines are parallel.
• CThey are neither parallel nor perpendicular.

Q4:

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.

Q5:

If and the slope of , find the slope of .

• A
• B
• C
• D

Q6:

If is a parallelogram, where and , find the slope of .

• A
• B
• C
• D

Q7:

Let be the line passing by the points and , and the perpendicular to that passes through the origin . What is the measure of the positive angle that makes with the positive -axis? Give your answer to the nearest second.

• A
• B
• C
• D

Q8:

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

Q9:

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

Q10:

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

• A
• B
• C
• D