ACT Math : Perpendicular Lines

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #2 : How To Find Out If Lines Are Perpendicular

Line , which follows the equation , intersects line  at . If line  also passes through , are  and  perpendicular?

Possible Answers:

Yes, because the product of their slopes is not .

No, because the product of their slopes is 

No, because the product of their slope is not .

Yes, because the product of their slopes is .

Correct answer:

Yes, because the product of their slopes is .

Explanation:

The product of perpendicular slopes is always . Knowing this, and seeing that the slope of line  is , we know any perpendicular line will have a slope of .

Since line  passes through  and , we can use the slope equation:

Since the two slopes' product is , the lines are perpendicular.

Example Question #3 : How To Find Out If Lines Are Perpendicular

Are the following two lines perpendicular:

 and

Possible Answers:

Correct answer:

Explanation:

For two lines to be perpendicular they have to have slopes that multiply to get . The slope is found from the  in the general equation: .

For the first line,  and for the second  and so the lines are not perpendicular.

Example Question #2 : How To Find Out If Lines Are Perpendicular

Which of the following equations represents a line that is perpendicular to the line with points  and ?

Possible Answers:

Correct answer:

Explanation:

If lines are perpendicular, then their slopes will be negative reciprocals.

First, we need to find the slope of the given line.

 

Because we know that our given line's slope is , the slope of the line perpendicular to it must be .

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