Lines and Angles Worksheets

**Page 2**

11.

Find the slope of the line passing through the points A (7, 9) and B (9, 13).

a. | - $\frac{1}{2}$ | ||

b. | - 2 | ||

c. | $\frac{1}{2}$ | ||

d. | 2 |

=

[Use the slope formula.]

Correct answer : (4)

12.

If $t$ > 1and $m$ is the slope of the line joining the points ($\frac{2}{{t}^{2}}$ , $\frac{4}{t}$) and (2$t$^{2} , 4$t$), then which of the following is correct?

a. | $m$ =1 | ||

b. | $m$ > 1 | ||

c. | $m$ < 1 | ||

d. | $m$ =2 |

Slope of line joining P,Q =

[Use the slope formula.]

=

So,

[Cancel the common factor.]

[ For

So,

Correct answer : (3)

13.

Find the values of $k$ such that the points ($k$ + 2, 2), (2$k$ + 2, 4) and (2$k$ + 3, 2$k$ + 1) are collinear.

a. | - $\frac{1}{2}$ , 2 | ||

b. | $\frac{1}{2}$ , 2 | ||

c. | $\frac{1}{2}$ , -2 | ||

d. | - $\frac{1}{2}$ , -2 |

Slope of line joining A, B = slope of line joining B,C .

[The three points A, B, C are collinear.]

[Use the slope formula.]

2

(2

[Factor.]

Correct answer : (1)

14.

What is the slope of the line 4$x$ + 9$y$ + 13 = 0?

a. | $\frac{9}{4}$ | ||

b. | $\frac{4}{9}$ | ||

c. | - $\frac{4}{9}$ | ||

d. | - $\frac{9}{4}$ |

[Solve for

As the above equation is in the slope intercept form

Correct answer : (3)

15.

What is the equation of the line passing through the points (2, 5) and (5, 2)?

a. | $x$ + $y$ + 3 = 0 | ||

b. | $x$ + $y$ - 7 = 0 | ||

c. | $x$ - $y$ + 7 = 0 | ||

d. | $x$ - $y$ + 3 = 0 |

The slope of the line passing through the points A and B is

[Use the slope formula.]

=

The equation of the line passing through A(

[Slope point form.]

Correct answer : (2)

16.

What is the equation of the line passing through (- 3, - 7) with the slope 5?

a. | 5$x$ - $y$ + 8 = 0 | ||

b. | 5$x$ - $y$ + 22 = 0 | ||

c. | $x$ - 5$y$ - 8 = 0 | ||

d. | $x$ - 5$y$ - 22 = 0 |

Let L be the line with the slope

If the line L passes through A then its equation is

[Slope point form.]

5

Correct answer : (1)

17.

Find the equation of the line with slope 7 and $y$ - intercept 11.

a. | 7$x$ - $y$ - 11 = 0 | ||

b. | $x$ - 7$y$ - 11 = 0 | ||

c. | 7$x$ - $y$ + 11 = 0 | ||

d. | $x$ - 7$y$ + 11 = 0 |

So, the equation of line L is

[Slope - intercept form.]

7

Correct answer : (3)

18.

What is the equation of the line which has 7 and - 8 as the $x$, $y$ - intercepts?

a. | 8$x$ + 7 $y$ - 56 = 0 | ||

b. | 8$x$ + 7 $y$ + 56 = 0 | ||

c. | 8$x$ - 7 $y$ - 56 = 0 | ||

d. | 8$x$ - 7 $y$ + 56 = 0 |

Let the equation of line L be

[Slope -intercept form.]

Substitute

[For

Substitute

[For

[

- (

[

So, the equation of the line L is

8

Correct answer : (3)

19.

What is the equation of the line passing through (6, 12) and has an angle of inclination $\frac{3\pi}{4}$?

a. | $x$ + $y$ - 18 = 0 | ||

b. | 6 $x$ + $y$ = 18 | ||

c. | $x$ - $y$ + 18 = 0 | ||

d. | 6 $x$ - $y$ = 0 |

The slope of the line L =

[Use the slope definition.]

Equation of the line L is

[Slope point form.]

Correct answer : (1)

20.

What is the equation of a vertical line whose $x$ - intercept is 3?

a. | $x$ = 3 | ||

b. | $x$ + $y$ = 3 | ||

c. | $y$ = 3 | ||

d. | $x$ - $y$ = 3 |

Equation of line L is

[Equation of a vertical line.]

Since

Since the line L passes through (3, 0), 3 =

[Substitute 3 for

So, the equation of the line L is

Correct answer : (1)