SSAT Upper Level Math : Properties of Parallel and Perpendicular Lines

Study concepts, example questions & explanations for SSAT Upper Level Math

Example Questions

Example Question #1 : Properties Of Parallel And Perpendicular Lines

Three lines are drawn on the coordinate plane.

The green line has slope , and -intercept .

The blue line has slope , and  -intercept .

The red line has slope , and -intercept .

Which two lines are perpendicular to each other?

Possible Answers:

It cannot be determined from the information given.

The blue line and the red line are perpendicular.

The blue line and the green line are perpendicular.

No two of these lines are perpendicular.

The green line and the red line are perpendicular.

Correct answer:

The blue line and the red line are perpendicular.

Explanation:

To demonstrate two perpendicular lines, multiply their slopes; if their product is , then the lines are perpendicular (the -intercepts are irrelevant).

The products of these lines are given here.

Blue and green lines: 

Red and green lines: 

Blue and red lines: 

It is the blue and red lines that are perpendicular.

We can also see that their slopes are negative reciprocals, indicating perpendicular lines.

Example Question #2 : Properties Of Parallel And Perpendicular Lines

Two perpendicular lines intersect at point . One line also includes point . What is the slope of the other line?

Possible Answers:

Insufficient information is given to answer the question.

Correct answer:

Explanation:

The slopes of two perpendicular lines are the opposites of each other's reciprocals. 

To find the slope of the first line substitute  in the slope formula:

The slope of the first line is , so the slope of the second line is the opposite reciprocal of this, which is .

Example Question #3 : Properties Of Parallel And Perpendicular Lines

Two perpendicular lines intersect at the origin; one line also passes through point . What is the slope of the other line?

Possible Answers:

Insufficient information is given to solve the problem.

Correct answer:

Explanation:

The slopes of two perpendicular lines are the opposites of each other's reciprocals. 

To find the slope of the first line, substitute  in the slope formula:

The slope of the first line is , so the slope of the second line is the opposite reciprocal of this, which is .

Example Question #4 : Properties Of Parallel And Perpendicular Lines

Which of the following lines is perpendicular to the line ?

Possible Answers:

Correct answer:

Explanation:

All we care about for this problem is the slopes of the lines...the x- and y-intercepts are irrelevant.

Remember that the slopes of perpendicular lines are opposite reciprocals. By putting the given equation into  form, we can see that its slope is . So we are looking for a line with a slope of .

The equation  can be put into the form , and so we know that it is perpendicular to the given line.

Learning Tools by Varsity Tutors