### All High School Math Resources

## Example Questions

### 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 .

**Possible Answers:**

**Correct answer:**

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 #2 : Perpendicular Lines

Find the equation of a line perpendicular to

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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 #5 : Perpendicular Lines

What line is perpendicular to through ?

**Possible Answers:**

**Correct answer:**

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 #6 : Perpendicular Lines

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

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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

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