﻿ Distance and Midpoint Worksheet | Problems & Solutions

# Distance and Midpoint Worksheet

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)

2.
Find the distance between the points O(0, 0) and P(18, 24).
 a. 30 b. 31 c. 32 d. 29

3.
What is the distance between the points Q(0, 4) and R(0, - 2)?
 a. 11 b. 7 c. 2 d. 6

4.
Find the distance between the points B(- 3, - 4) and C(10, - 4).
 a. 14 b. 13 c. 12 d. 15

5.
Find the distance between the points B(- 4, 6) and C(13, 6).
 a. 18 b. 15 c. 17 d. 19

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

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)

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)

#### Solution:

The coordinates of M are (5, 5) and the coordinates of N are (-4, -4).

Midpoint of a line-segment with endpoints (x1, y1) and (x2, y2) is [(x1 + x2)/2, (y1 + y2)/2]
[Use the midpoint formula.]

Midpoint of MN = (5+(-4)2, 5+(-4)2)
[Replace (x1, y1) with (5, 5) and (x2, y2) with (-4, -4).]

= (12, 12)
[Simplify .]

The midpoint of the line-segment MN = (1 / 2, 1 / 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

#### Solution:

The coordinates of A are (2p, 3p).

Distance of a point (x, y) from origin is √(x2 + y2)
[Write the distance formula.]

Distance of A from origin = √[(2p)2 + (3p)2)]
[Replace (x, y) with (2p, 3p.]

= √(4p2 + 9p2)
[Evaluate powers.]

= √(13p2)

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

√(13p2) = 2√13
[Equate distances.]

13p2 = 4 x 13
[Squaring on both sides.]

p2 = 4
[Divide each side by 13.]

p = √4

= ± 2
[Find the square root.]

The value of p is 2 or -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

#### Solution:

From the graph, the coordinates of A are (-3, 4) and C are (4, -1).

Distance between the line-segment with endpoints (x1, y1) and (x2, y2) is √(x2 - x1)2 + (y2 - y1)2

Distance between A and C = √[(4 - (-3))2 + (-1 - 4)2]
[Replace (x1, y1) with (-3, 4) and (x2, y2) with (4, -1).]

= √[(72 + (-5)2)]
[Subtract.]

= √(49 + 25)
[Evaluate powers.]

= √74