Question

1. find the distance between g(-3,5) and h(6,-1).

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Here, $(x_1,y_1)=(-3,5)$ and $(x_2,y_2)=(6,-1)$.

Step2: Substitute values

$d=\sqrt{(6-(-3))^2+((-1) - 5)^2}=\sqrt{(6 + 3)^2+(-6)^2}=\sqrt{9^2+(-6)^2}=\sqrt{81 + 36}=\sqrt{117}$.

Step3: Simplify

$\sqrt{117}=\sqrt{9\times13}=3\sqrt{13}$.

Answer:

$3\sqrt{13}$