Question

question
find the distance between the two points in simplest radical form.
(-2,3) and (6,-4)
answer attempt 1 out of 2

Explanation:

Step1: Identify the 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 the values

Let $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(6,-4)$. Then $x_2 - x_1=6-(-2)=8$ and $y_2 - y_1=-4 - 3=-7$.

Step3: Calculate the squares

$(x_2 - x_1)^2=8^2 = 64$ and $(y_2 - y_1)^2=(-7)^2 = 49$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 49=113$.

Step5: Find the distance

$d=\sqrt{113}$.

Answer:

$\sqrt{113}$