Question

calculate the distance between the points p=(-9, 7) and f=(-1, 2) in the coordinate plane. give an exact answer (not a decimal approximation). distance:

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-9,y_1 = 7,x_2=-1,y_2 = 2$.

Step2: Substitute values

$d=\sqrt{(-1-(-9))^2+(2 - 7)^2}=\sqrt{(-1 + 9)^2+(2-7)^2}=\sqrt{(8)^2+(-5)^2}$.

Step3: Calculate squares and sum

$\sqrt{64 + 25}=\sqrt{89}$.

Answer:

$\sqrt{89}$