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# Distance Between Two Points on a Graph Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Distance Between Two Points on a Graph Study Guide.

## Distance Between Two Points on a Graph Practice Questions

### Problems

Find the distance between each pair of points.

1. (2,8) and (8,16)
2. (–5,1) and (4,13)
3. (3,4) and (8,3)
4. (–7,–1) and (–1,–3)
5. (–3,–5) and (5,–13)

### Solutions

1. Use the distance formula to find the distance between (2,8) and (8,16). Because (2,8) is the first point, x1 is 2 and y1 is 8. (8,16) is the second point, so x2 is 8 and y2 is 16:

D = √(x2x1)2 + (y2y1)2

D = √(8 – 2)2 + (16 – 8)2

D = √(6)2 + (8)2

D = √36 + 64

D = √36 + 100

D = 10 units

2. Use the distance formula to find the distance between (–5,1) and (4,13). Because (–5,1) is the first point, x1 is –5 and y1 is 1. (4,13) is the second point, so x2 is 4 and y2 is 13:

D = √(x2x1)2 + (y2y1)2

D = √(4 – (–5))2 + (13 – 1)2

D = √81 + 144

D = √225

D = 15 units

3. Use the distance formula to find the distance between (3,4) and (8,3). Because (3,4) is the first point, x1 is 3 and y1 is 4. (8,3) is the second point, so x2 is 8 and y2 is 3:

D = √(x2x1)2 + (y2y1)2

D = √(8 – 3)2 + (3 – 4)2

D = √(5)2 + (–1)2

D = √25 + 1

D = √26 units

4. Use the distance formula to find the distance between (–7,–1) and (–1 –3). Because (–7,–1) is the first point, x1 is –7 and y1 is –1. (–1,–3) is the second point, so x2 is –1 and y2 is –3:

D = √(x2x1)2 + (y2y1)2

D = √(–1 – (–7))2 + (–3 – (–1))2

D = √(6)2 + (–2)2

D = √36 + 4

D = √40

The number 40 is divisible by 4, which is a perfect square. Because 40 = (4)(10), √40 = √410 = 2 √10 units

5. Use the distance formula to find the distance between (–3,–5) and (5,–13). Because (–3,–5) is the first point, x1 is –3 and y1 is –5. (5,–13) is the second point, so x2 is 5 and y2 is –13:

D = √(x2x1)2 + (y2y1)2

D = √(5 – (–3))2 + (–13 – (–5))2

D = √(8)2 + (–8)2

D = √64 + 64

D = √128

The number 128 is divisible by 64, which is a perfect square. Because 128 = (64)(2), √128 = √642 = 8√2 units.

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