Question

find the distance between the points a(13, 2) and b(7, 10).
the distance between the two points is \boxed{}.

Explanation:

Step1: Recall distance formula

The distance $d$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given coordinates

Let $(x_1,y_1)=(13,2)$ and $(x_2,y_2)=(7,10)$.
$d=\sqrt{(7-13)^2+(10-2)^2}$

Step3: Calculate differences

$d=\sqrt{(-6)^2+(8)^2}$

Step4: Compute squares and sum

$d=\sqrt{36+64}=\sqrt{100}$

Step5: Simplify square root

$d=10$

Answer:

10