# High School Math : Perpendicular Lines

## Example Questions

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### Example Question #1 : Perpendicular Lines

Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points and .

Explanation:

Find the slope of the line through the two points. It is .

Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula  . Isolate for

### Example Question #1 : How To Find The Equation Of A Perpendicular Line

Find the equation of a line perpendicular to

Explanation:

Since a perpendicular line has a slope that is the negative reciprocal of the original line, the new slope is . There is only one answer with the correct slope.

### Example Question #3 : Perpendicular Lines

Find the equation (in slope-intercept form) of a line perpendicular to

Explanation:

First, find the slope of the original line, which is . You can do this by isolating for  so that the equation is in slope-intercept form. Once you find the slope, just replace the  in the original equation withe the negative reciprocal (perpendicular lines have a negative reciprocal slope for each other). Thus, your answer is

### Example Question #4 : Perpendicular Lines

Given the equation  and the point , find the equation of a line that is perpendicular to the original line and passes through the given point.

Explanation:

In order for two lines to be perpendicular, their slopes must be opposites and recipricals of each other. The first step is to find the slope of the given equation:

Therefore, the slope of the perpendicular line must be . Using the point-slope formula, we can find the equation of the new line:

### Example Question #31 : Algebra I

What line is perpendicular to through ?

Explanation:

Perdendicular lines have slopes that are opposite reciprocals.  The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept:

or , so .

Thus , or .

### Example Question #1 : How To Find The Equation Of A Perpendicular Line

What is the equation, in slope-intercept form, of the perpendicular bisector of the line segment that connects the points  and ?

Explanation:

First, calculate the slope of the line segment between the given points.

We want a line that is perpendicular to this segment and passes through its midpoint. The slope of a perpendicular line is the negative inverse. The slope of the perpendicular bisector will be .

Next, we need to find the midpoint of the segment, using the midpoint formula.

Using the midpoint and the slope, we can solve for the value of the y-intercept.

Using this value, we can write the equation for the perpendicular bisector in slope-intercept form.

### Example Question #7 : Perpendicular Lines

What line is perpendicular to through ?

Explanation:

The equation is given in the slope-intercept form, so we know the slope is .  To have perpendicular lines, the new slope must be the opposite reciprocal of the old slope, or

Then plug the new slope and the point into the slope-intercept form of the equation:

so so

So the new equation becomes:  and in standard form

### Example Question #1 : How To Find The Slope Of A Perpendicular Line

A line passes through the points  and .  If a new line is drawn perpendicular to the original line, what will its slope be?

Explanation:

The original line has a slope of , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

### Example Question #1 : How To Find The Slope Of A Perpendicular Line

Which of the following is the equation of a line that is perpendicular to the line  ?

Explanation:

Perpendicular lines have slopes that are the opposite reciprocals of each other. Thus, we first identify the slope of the given line, which is  (since it is in the form , where  represents slope).

Then, we know that any line which is perpendicular to this will have a slope of .

Thus, we can determine that  is the only choice with the correct slope.

### Example Question #1 : Perpendicular Lines

What will be the slope of the line perpendicular to ?