Question

Find the distance between the following pairs of points $(-4,5)$ and $(-12,3)$.

Answer 1

the distance between the two points is given by $(x_1,y_1)$ and $(x_2,y_2)$ is

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

Here, the given points are $(-4,5)$ and $(-12,3)$, therefore,

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

$d=\sqrt{{(-12-(-4\left)\right)}^2+{(3-5)}^2}$

$d=\sqrt{{(-12+4)}^2+{(-2)}^2}$

$d=\sqrt{{(-8)}^2+{(-2)}^2}$

$d=\sqrt{64+4}=\sqrt{68}$

$d=\sqrt{2^2\times 17}=2\sqrt{17}$

Hence, the distance is $2\sqrt{17}$ units.