Distance and Midpoint Worksheet

**Page 1**

1.

Find the coordinates of the midpoint of the line segment whose end points are (2, 1) and (6, 5).

a. | (8, 6) | ||

b. | (3, 4) | ||

c. | (4, 4) | ||

d. | (4, 3) |

Correct answer : (4)

2.

Find the distance between the points O(0, 0) and P(18, 24).

a. | 30 | ||

b. | 31 | ||

c. | 32 | ||

d. | 29 |

Correct answer : (1)

3.

What is the distance between the points Q(0, 4) and R(0, - 2)?

a. | 11 | ||

b. | 7 | ||

c. | 2 | ||

d. | 6 |

Correct answer : (4)

4.

Find the distance between the points B(- 3, - 4) and C(10, - 4).

a. | 14 | ||

b. | 13 | ||

c. | 12 | ||

d. | 15 |

Correct answer : (2)

5.

Find the distance between the points B(- 4, 6) and C(13, 6).

a. | 18 | ||

b. | 15 | ||

c. | 17 | ||

d. | 19 |

Correct answer : (3)

6.

What is the distance between the points (4, 4) and (16,20)?

a. | 400 units | ||

b. | 144 units | ||

c. | 256 units | ||

d. | 20 units |

Correct answer : (4)

7.

Find the coordinates of the midpoint of the segment with the end points (- 4, 3) and (1, 1).

a. | (- 3, 4) | ||

b. | (1, 1) | ||

c. | (- $\frac{3}{2}$, 2) | ||

d. | ($\frac{3}{2}$, 2) |

Correct answer : (3)

8.

Find the midpoint of the line-segment MN.

a. | (2, 1) | ||

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

c. | (1, 1) | ||

d. | (1, 2) |

Midpoint of a line-segment with endpoints (

[Use the midpoint formula.]

Midpoint of MN = (

[Replace (

= (

[Simplify .]

The midpoint of the line-segment MN = (

Correct answer : (2)

9.

The coordinates of A are (2$p$, 3$p$) and the distance from origin to A is 2√13 units. Find the value of $p$.

a. | 4 or -4 | ||

b. | 2 or -2 | ||

c. | 3 or -3 | ||

d. | None of the above |

Distance of a point (

[Write the distance formula.]

Distance of A from origin = √[(2

[Replace (

= √(4

[Evaluate powers.]

= √(13

[add.]

The distance of point A from origin is 2√13 units.

√(13

[Equate distances.]

13

[Squaring on both sides.]

[Divide each side by 13.]

= ± 2

[Find the square root.]

The value of

Correct answer : (2)

10.

Find the length of the diagonal AC of the parallelogram ABCD in the figure.

a. | 8.6 units | ||

b. | 4.5 units | ||

c. | 5.8 units | ||

d. | None of the above |

Distance between the line-segment with endpoints (

Distance between A and C = √[(4 - (-3))

[Replace (

= √[(7

[Subtract.]

= √(49 + 25)

[Evaluate powers.]

= √74

[Add.]

= 8.6

Length of the line-segment = Distance between the endpoints of the segment.

The length of the diagonal AC is 8.6 units.

Correct answer : (1)