Question

find the distance between the points. (9, 6), (6, -1)

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(9,6)$ and $(x_2,y_2)=(6, - 1)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. So, $x_2 - x_1=6 - 9=-3$ and $y_2 - y_1=-1 - 6=-7$.

Step3: Square the differences

Square the results from Step 2. $(-3)^2 = 9$ and $(-7)^2=49$.

Step4: Sum and take square - root

Sum the squared values: $9 + 49 = 58$. Then, $d=\sqrt{58}$.

Answer:

$\sqrt{58}$