# SSAT Upper Level Math : How to find out if lines are perpendicular

## Example Questions

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

Two perpendicular lines intersect at the point . One line passes through point ; the other passes through point . Evaluate .

Explanation:

The line that passes through  and  has slope

.

The line that passes through  and  , being perpendicular to the first, has as its slope the opposite reciprocal of , or

Therefore, to find , we use the slope formula and solve for :

### Example Question #51 : Lines

A line has the following equation:

Which of the following could be a line that is perpendicular to this given line?

Explanation:

First, put the equation of the given line in the  form to find its slope.

Since the slope of the given line is , the slope of the line that is perpendicular must be its negative reciprocal, .

Now, put each answer choice in  form to see which one has a slope of .

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

Which of the following lines is perpendicular to the line ?

Explanation:

Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.

The slope of this line is . The negative reciprocal will be , which will be the slope of the perpendicular line.

Now we need to find the answer choice with this slope by converting to slope-intercept form.

This equation has a slope of , and must be our answer.

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

Which of the following lines is perpindicular to

Explanation:

When determining if a two lines are perpindicular, we are only concerned about their slopes. Consider the basic equation of a line, , where m is the slope of the line. Two lines are perpindicular to each other if one slope is the negative and reciprocal of the other.

The first step of this problem is to get it into the form, , which is . Now we know that the slope, m, is . The reciprocal of that is , and the negative of that is . Therefore, any line that has a slope of  will be perpindicular to the original line.

### Example Question #1 : 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 ?

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 .

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

Which of the following lines is perpendicular to a line with a slope ?

Not enough information provided

Explanation:

For a given line  with a slope , any perpendicular line would have a slope , or the negative reciprocal of .

Given that  in this instance, we can conclude that the slope of a perpendicular line would be . Therefore, the equation that contains this slope is

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

Which of the following lines would be perpendicular to ?

Not enough information provided to solve

Explanation:

For a given line  with a slope , any perpendicular line would have a slope , or the negative reciprocal of .

Given that  in this instance, we can conclude that the slope of a perpendicular line would be . Given the perpendicular slope, we can now conclude that the perpendicular line is .

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

A given line has the equation . What is the slope of any line that is perpendicular to this line?