Find the distance between the points (5, 7) and (8, - 5).
 

Given points are (5, 7) and (8, - 5).

To find the distance between two points , we can use distance formula:

d =  $\sqrt{({\mathrm{x}}_2-{\mathrm{x}}_1{)}^{2 }+{({\mathrm{y}}_2-{\mathrm{y}}_1)}^2 }$

Where $(x_1, y_1) and (x_2,y_2)$coordinates of two points.

Here, $(x_1, y_1) = (5, 7) and (x_2,y_2) = (8,-5)$

 On substitution, we get:

$=$ $\sqrt{{(8-5)}^2+{(-5-7)}^2}$
$=\sqrt{{\left(3\right)}^2+{(-12)}^2}$
$=\sqrt{9+144}$
$=\sqrt{153}$  units

Therefore, the distance between  the points (5, 7) and (8, - 5) is $\sqrt{153 }$ Units