Lines and Angles Worksheets

**Page 1**

1.

Find the inclination of the line $y$ = $x$ + 32.

a. | 90 ^{o} | ||

b. | 45 ^{o} | ||

c. | 60 ^{o} | ||

d. | 30 ^{o} |

Slope =

[Compare with

θ = tan

So, the inclination of the line is θ = 45

Correct answer : (2)

2.

What is the measure of the angle between the two lines having the slopes - 7 and $\frac{1}{7}$.

a. | 45 ^{o} | ||

b. | 60 ^{o} | ||

c. | 30 ^{o} | ||

d. | 90 ^{o} |

The angle between the two lines is θ =

[Use the formula to find the angle between the two lines.]

=

= 90

Correct answer : (4)

3.

If a non vertical line has an inclination θ with the positive $x$-axis, then find the slope $m$ of the line in terms of θ.

a. | cosec $\theta $ | ||

b. | cot $\theta $ | ||

c. | tan $\theta $ | ||

d. | sin $\theta $ |

Correct answer : (3)

4.

Find the measure of the angle between two lines having slopes 7 and $\frac{1}{7}$ .

a. | tan ^{-1}(48) | ||

b. | tan ^{-1}(49) | ||

c. | tan ^{-1}($\frac{24}{7}$) | ||

d. | tan ^{-1}($\frac{1}{14}$) |

The angle between the two lines is θ =

[Use the formula to find the angle between two lines.]

=

= tan

Correct answer : (3)

5.

Find the measure of the angle between the two lines 8$x$ + 9$y$ = 1 and 4$x$ + 7$y$ = 1.

a. | - tan ^{-1}($\frac{4}{19}$) | ||

b. | tan ^{-1}($\frac{1}{95}$ ) | ||

c. | tan ^{-1}(20 ) | ||

d. | tan ^{-1}(7 ) |

[Convert into

The slopes of the lines are

[Write the slopes of the two lines.]

The angle between the given lines is θ =

[Use the formula to find the angle between the lines.]

= - tan

Correct answer : (1)

6.

What is the measure of the angle between the two lines 5$x$ + $y$ + 4 = 0 and 5$x$ - $y$ - 3 = 0?

a. | tan ^{-1}(24 ) | ||

b. | - tan ^{-1}($\frac{5}{12}$) | ||

c. | tan ^{-1}($\frac{5}{12}$) | ||

d. | tan ^{-1}(10 ) |

[Convert it into

The slopes of the two lines are

[Write the slopes of the two lines.]

The angle between the given lines is θ =

[Use the formula to find the angle between the two lines.]

= tan

Correct answer : (3)

7.

What is the perpendicular distance between the point (2, 2) and the line 12$x$ + 16$y$ + 2 = 0.

a. | 20 units | ||

b. | $\frac{1}{20}$ units | ||

c. | 58 units | ||

d. | $\frac{29}{10}$units |

[The perpendicular distance from the point P (

=

Correct answer : (4)

8.

What is the slope of the line on which for every point the ordinate is same?

a. | Undefined | ||

b. | Infinitely large | ||

c. | Infinitely small |

So, let P(14,9) and Q(19,9) be the two points on line L.

Slope of line L = Slope of line joining P,Q =

=

[Use the slope formula.]

=

Correct answer : (2)

9.

The angle of inclination of a line is $\frac{3\pi}{4}$ . What is the slope of the line?

a. | -1 | ||

b. | 1 | ||

c. | -2 | ||

d. | 2 |

Slope of the line =

[Use the definition of slope.]

= tan

Correct answer : (1)

10.

What is the slope of a line on which for every point the $x$ coordinate is same?

a. | Infinitely small | ||

b. | Undefined | ||

c. | Infinitely large |

So, let A(3, 6), B(3, 9) be two points on line L.

Slope of line L = Slope of line joining A,B =

[Use the slope formula.]

=

=

[Division by 0 is not defined]

Correct answer : (3)

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