Question

find the distance between the points g( - 5,4) and h(2,0). answer in simplest exact form. the exact distance between the two points is

Explanation:

Step1: Identify 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: Assign values

Let $(x_1,y_1)=(-5,4)$ and $(x_2,y_2)=(2,0)$. Then $x_2 - x_1=2-(-5)=7$ and $y_2 - y_1=0 - 4=-4$.

Step3: Calculate distance

$d=\sqrt{(7)^2+(-4)^2}=\sqrt{49 + 16}=\sqrt{65}$.

Answer:

$\sqrt{65}$