Question

consider the following pair of points.
(9,4) and (-8,10)
step 1 of 2: determine the distance between the two points.

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, $x_1 = 9,y_1 = 4,x_2=-8,y_2 = 10$.

Step2: Substitute values

First, calculate $(x_2 - x_1)$ and $(y_2 - y_1)$: $x_2 - x_1=-8 - 9=-17$, $y_2 - y_1=10 - 4 = 6$. Then, $(x_2 - x_1)^2+ (y_2 - y_1)^2=(-17)^2+6^2=289 + 36=325$.

Step3: Calculate distance

$d=\sqrt{325}=\sqrt{25\times13}=5\sqrt{13}$.

Answer:

$5\sqrt{13}$