Algebra 1 : How to find out if lines are perpendicular

Study concepts, example questions & explanations for Algebra 1

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Example Question #1 : How To Find Out If Lines Are Perpendicular

Which ONE of these statements about the lines defined by the following equations is TRUE?

Line 1: 

Line 2: 

Possible Answers:

The slopes of the two lines are identical.

The lines intersect and are perpendicular.

The lines intersect at the point .

The lines do not intersect.

The lines intersect only once because they are parallel. 

Correct answer:

The lines intersect and are perpendicular.

Explanation:

The TRUE statement:

"The lines intersect and are perpendicular." This is true because the slopes of the two lines are opposite-reciprocals of each other.

The FALSE statements:

"The lines intersect at the point ." The lines actually intersect at the point . Neither line touches the point , as their y-intercepts are given in their respective equations as and .

"The slopes of the two lines are identical." This is not true because the slope of Line 1 is  whereas the slope of Line 2 is .

"The lines do not intersect." The lines would need to be parallel (i.e., have the same slope) for this to be the case, but the lines do not have the same slope.

"The lines intersect only once because they are parallel." Parallel lines never intersect, so this statement cannot be made of any set of two lines.

Example Question #1 : How To Find Out If Lines Are Perpendicular

Which equation describes a line that is perendicular to 

Possible Answers:

None of these answers describe a line that is perpendicular to .

Correct answer:

Explanation:

To find out if two lines are perpendicular, we just need to see whether their slopes are opposite reciprocals of each other.

The reciprocal of 6 is , so the opposite reciprocal is .

The only answer choice with a slope of  is

 

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

Determine if the lines  and  are perpendicular.

Possible Answers:

The lines are not perpendicular

There is not enough information to determine the answer

The lines are perpendicular

Correct answer:

The lines are perpendicular

Explanation:

For lines to be perpendicular, the slopes need to be negative reciprocals of each other.  For the line , the slope is 1.  For a line to be perpendicular to it, it will need to have a slope of .  Since the line  has a slope of -1, the lines are perpendicular to each other.

Example Question #4 : How To Find Out If Lines Are Perpendicular

Which of these lines is perpendicular to 

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. If you convert the given line to the  form, you get 

which indicates a slope of . Thus, the slope of the perpendicular line must be , which is the negative reciprocal of . The only line with a slope of  is 

.

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

Which of the following equations describes a line perpendicular to the line ?

Possible Answers:

Correct answer:

Explanation:

The line  is a vertical line.  Therefore, a perpendicular line is going to be horizontal and have a slope of zero.  

The equation  is such a line.  

The lines  and  are both vertical lines, while the lines  and  have slopes of  and , respectively.

Example Question #6 : How To Find Out If Lines Are Perpendicular

Which of these lines is perpendicular to ?

Possible Answers:

Correct answer:

Explanation:

Perpendicular lines have slopes that are negative reciprocals of one another. Since all of these lines are in the format, it is easy to determine their slopes, or .

The slope of the original line is , so any line that is perpendicular to it must have a slope of .

The only line with a slope of is .

Example Question #7 : How To Find Out If Lines Are Perpendicular

Which option best describes the lines and

Possible Answers:

parallel

not parallel or perpendicular

the same line

perpendicular

Correct answer:

perpendicular

Explanation:

To best compare these two lines, it will be easiest to put the second one into slope-intercept form. That way we can more easily tell what the slope is. Right now it looks like , and we want to solve that for y. First we can add 8 to both sides:

we would like this to be in the form y=, so divide both sides by -2:

to simplify the left side, divide each term individually by -2.

, and .

This gives us the equation , which means the slope of the second line is . The slope of the first line was 2, so this slope is its negative reciprocal.

That means these two lines are perpendicular.

Example Question #4 : How To Find Out If Lines Are Perpendicular

Which of the following lines could be perpendicular to the following:

Possible Answers:

None of the available answers

Correct answer:

Explanation:

The only marker for whether lines are perpendicular is whether their slopes are the opposite-reciprocal for the other line's slope. The -intercept is not important. Therefore, the line perpendicular to  will have a slope of  or 

Example Question #5 : How To Find Out If Lines Are Perpendicular

Find a line perpendicular to the line with the equation:

Possible Answers:

Correct answer:

Explanation:

Lines can be written in the slope-intercept format:

In this format,  equals the line's slope and  represents where the line intercepts the y-axis.

In the given equation:

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

Second, we need to rewrite it with the opposite sign.

Only one of the choices has a slope of .

Example Question #10 : How To Find Out If Lines Are Perpendicular

Find a line perpendicular to the line with the equation:

Possible Answers:

Correct answer:

Explanation:

Lines can be written in the slope-intercept format:

In this format,  equals the line's slope and  represents where the line intercepts the y-axis.

In the given equation:

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

Second, we need to rewrite it with the opposite sign.

Only one of the choices has a slope of .

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