Question

find the distance between (-2,-4) and (4,-10). provide an answer accurate to the nearest hundredth.

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, $(x_1,y_1)=(-2,-4)$ and $(x_2,y_2)=(4,-10)$.

Step2: Substitute values

$d=\sqrt{(4 - (-2))^2+((-10)-(-4))^2}=\sqrt{(4 + 2)^2+(-10 + 4)^2}=\sqrt{6^2+(-6)^2}$.

Step3: Calculate squares and sum

$\sqrt{36+36}=\sqrt{72}$.

Step4: Simplify and round

$\sqrt{72}\approx8.49$.

Answer:

$8.49$