Question

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

Explanation:

Step1: Recall distance formula

The distance formula 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: Identify coordinates

Here, $x_1=-5,y_1 = 4,x_2=2,y_2 = 6$.

Step3: Substitute values

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

Step4: Calculate

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

Answer:

$\sqrt{53}$