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

Answer:

(a) 5

(b) 10

(c) 13

Step-by-step 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)

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

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

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

(c) (-4, 6) and (1,-6)​

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