Question

Find the distance between the following pairs of points:

A. $(2,3),(4,1)$

B. $(-5,7),(-1,3)$

C. $(a,b),(-a,-b)$

Answer 1

Using distance formula if two points $(x_1,y_1)$ and $(x_2,y_2)$ are given.

$d=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$

Part (A).

Given points are $(2,3),(4,1)$

Then distance $d=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$

$d=\sqrt{{(2-4)}^2+{(3-1)}^2}$

$=\sqrt{{(-2)}^2+{\left(2\right)}^2}$

$=\sqrt{8}Ans.$

Part (B).

Given points are $(-5,7),(-1,3)$

Then distance $d=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$

$d=\sqrt{{(-5+1)}^2+{(7-3)}^2}$

$=\sqrt{{(-4)}^2+{\left(4\right)}^2}$

$=\sqrt{32}Ans.$

Part (C).

Given points are $(a,b),(-a,-b)$

Then distance $d=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$

$d=\sqrt{{(a+a)}^2+{(b+b)}^2}$

$=\sqrt{{\left(2a\right)}^2+{\left(2b\right)}^2}$

$=\sqrt{4(a^2+b^2)}$

$=2\sqrt{(a^2+b^2)}Ans.$