Question

what is the distance between the points (-1,4) and (7,-2)? > enter the answer in the space provided. use numbers instead of words. units

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: Substitute the values

Here $x_1=-1,y_1 = 4,x_2=7,y_2=-2$. So $d=\sqrt{(7-(-1))^2+((-2 - 4))^2}=\sqrt{(7 + 1)^2+(-6)^2}$.

Step3: Calculate the squares

$(7 + 1)^2=8^2 = 64$ and $(-6)^2=36$. Then $d=\sqrt{64 + 36}$.

Step4: Add the values inside the square - root

$64+36 = 100$. So $d=\sqrt{100}$.

Step5: Find the square - root

$\sqrt{100}=10$.

Answer:

10