Question

Find the distance between the two points in simplest radical form. (-5,8) and (-3, 1)

Answer 1

Given:

The two points are (-5,8) and (-3,1).

To find:

The distance between the given two points in simplest radical form.

Solution:

Distance formula: The distance between two points is

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

Using distance formula, the distance between (-5,8) and (-3,1) is

$d=\sqrt{(-3-(-5))^2+(1-8)^2}$

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

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

$d=\sqrt{4+49}$

$d=\sqrt{53}$

Therefore, the distance between two points (-5,8) and (-3,1) is $\sqrt{53}$ units.