Question

Find the distance between the following pairs of points. Give your answer correct to 2 decimal places if necessary.

(a) (2, 4) and (5, 0)
(b) (8, 1) and (2, -7)
(c) (-4, 6) and (1,-6)​

Answer 1

(a) 5

(b) 10

(c) 13

Explanation:

We know the distance between two points is:

d=
`\sqrt{(x_(2) -x_(1) )^(2) +(y_(2)-y_(1))^(2)}`

we have the following pairs of points:

(a) (2, 4) and (5, 0)

`d=\sqrt{(5 -2)^(2) +(0-4)^(2)} \\\\d=\sqrt{(3)^(2) +(-4)^(2)} \\\\d=√(9+16)\\\\d=√(25) = 5`

(b) (8, 1) and (2, -7)

`d=\sqrt{(2 -8)^(2) +(-7-1)^(2)} \\\\d=\sqrt{(-6)^(2) +(-8)^(2)} \\\\d=√(36+64)\\\\d=√(100) = 10`

(c) (-4, 6) and (1,-6)​

`d=\sqrt{(1 -(-4))^(2) +(-6-6)^(2)} \\\\d=\sqrt{(5)^(2) +(-12)^(2)} \\\\d=√(25+144)\\\\d=√(169) = 13`