Perpendicular Lines Worksheets

**Page 1**

1.

Is the line passing through the points (-3, 4) and (-5, 6) perpendicular to the line $y$ = $x$ + 5?

a. | Yes | ||

b. | No |

Slope of the line passing through the points (-3, 4) and (-5, 6) =

= -1

[Simplify.]

Slope of the line

Product of the slopes of the two lines = -1 x 1 = -1

[Multiply.]

Two lines are perpendicular, only if the product of their slopes is -1.

So, the two lines are perpendicular.

Correct answer : (1)

2.

Are the two lines $y$ = 2$x$ + 3 and $y$ = 2$x$ + 4 perpendicular?

a. | Yes | ||

b. | No |

The slope-intercept form of the equation of a line with slope

The two given lines are in slope-intercept form.

Slope of the line

[Compare with the equation in step 1.]

Slope of the line

[Compare with the equation in step 1.]

Product of the slopes of the two lines = 2 x 2 = 4

[Multiply.]

So, the two equations are not perpendicular.

Correct answer : (2)

3.

Are the two lines $y$ = 3$x$ + 2 and $y$ = -4$x$ + $\frac{2}{3}$ perpendicular?

a. | No | ||

b. | Yes |

The two given lines are in slope-intercept form.

Slope of the line

[Compare with the equation in step 1.]

Slope of the line

[Compare with the equation in step 1.]

Product of the slopes of two lines = 3 x (-4) = -12

[Multiply.]

Two lines are perpendicular, if the product of the slopes of the two lines is equal to -1.

The product of the slopes of the two lines is -12. So, they are not perpendicular.

Correct answer : (1)

4.

Is the line passing through the points (2, 3) and (-4, -5) perpendicular to the line $y$ = $\frac{\mathrm{3x}}{4}$ + 4?

a. | No | ||

b. | Yes |

So, the slope of the line passing through (2, 3) and (-4, -5) =

[Substitute

Slope of the line

[Slope = coefficient of

Product of the slopes of the two lines =

[Multiply.]

Two lines are perpendicular, if the product of their slopes is -1.

The product of the slopes of the two lines is 1. So, the two lines are not perpendicular.

Correct answer : (1)

5.

___ and ___ lines are always perpendicular to each other.

a. | Intersecting, non-intersecting | ||

b. | Horizontal, vertical | ||

c. | Parallel, skew | ||

d. | Parallel, transversal |

So, horizontal and vertical lines are perpendicular to each other.

Correct answer : (2)

6.

Write an equation of the line passing through the point (-3, -4) and perpendicular to the line $y$ = 5$x$ + 3.

a. | $y$ = - $\frac{1}{5}$($x$ + 3) | ||

b. | $y$ + 4 = - $\frac{1}{5}$($x$ + 3) | ||

c. | $y$ + 4 = $\frac{1}{5}$($x$ + 3) | ||

d. | None of the above |

Slope of the line

[Compare with the equation in step 1.]

Slope of the line perpendicular to

[Product of the slopes of perpendicular lines is -1.]

The equation of the line passing through the point (

[Substitute (

[Simplify the equation.]

The equation of the line passing through the point (-3, -4) is

Correct answer : (2)

7.

Which among the following are not the slopes of two perpendicular lines?

a. | 3 & $\frac{-1}{3}$ | ||

b. | 1 & -1 | ||

c. | $\frac{3}{4}$ & $\frac{-4}{3}$ | ||

d. | 8 & $\frac{1}{8}$ |

Among the choices, 8 x

[Multiply and simplify.]

So, 8 and

Correct answer : (4)

8.

Is the line passing through the points (-4, 5) and (-5, 9) perpendicular to the line $y$ = $\frac{\mathrm{x}}{4}$ + 5?

a. | Yes | ||

b. | No |

The slope of the line passing through the points (-4, 5) and (-5, 9) is

[Substitute

=

[Simplify the fraction.]

Slope of the line

[Slope = coefficient of

Product of the slopes of the two lines = -4 x

[Multiply.]

Two lines are perpendicular, if the product of their slopes is -1.

So, the two lines are perpendicular.

Correct answer : (1)

9.

Are the two lines $y$ = 5$x$ + 4 and $y$ = -5$x$ + 7 perpendicular?

a. | Yes | ||

b. | No |

The two given lines are in slope-intercept form.

Slope of the line

[Compare with the equation in step 1.]

Slope of the line y = -5

[Compare with the equation in step 1.]

Product of the slopes of the two lines = 5 x -5 = -25

[Multiply.]

Two lines are perpendicular, only if the product of their slopes is -1.

The product of the slopes of the two lines is -25. So, they are not perpendicular.

Correct answer : (2)

10.

Are the two lines $y$ = -5$x$ - 5 and $y$ = -5$x$ + 5 perpendicular?

a. | Yes | ||

b. | No |

The two given lines are in slope-intercept form.

Slope of the line

[Compare with the equation in step 1.]

Slope of the line

[Compare with the equation in step 1.]

Product of the slopes of the two lines = -5 x -5 = 25

[Multiply.]

The product of the slopes of the two lines is not equal to -1.

So, the two equations are not perpendicular.

Correct answer : (2)

More Perpendicular Lines Worksheets | |

Perpendicular Lines Worksheet | |