Question

find the distance between the points g(-5, 4) and h(2, 6). answer in simplest exact form.

the exact distance between the two points is \boxed{}

Explanation:

Step1: Recall distance formula

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

Step2: Assign coordinates

Let $(x_1,y_1)=(-5,4)$ and $(x_2,y_2)=(2,6)$

Step3: Substitute into formula

$d=\sqrt{(2-(-5))^2+(6-4)^2}=\sqrt{(7)^2+(2)^2}$

Step4: Simplify the expression

$d=\sqrt{49+4}=\sqrt{53}$

Answer:

$\sqrt{53}$