Question

find the distance between (-6, -4) and (-7, -8). 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, $x_1=-6,y_1 = - 4,x_2=-7,y_2=-8$.

Step2: Substitute values

$d=\sqrt{(-7-(-6))^2+(-8 - (-4))^2}=\sqrt{(-7 + 6)^2+(-8 + 4)^2}=\sqrt{(-1)^2+(-4)^2}$.

Step3: Calculate squares and sum

$\sqrt{(-1)^2+(-4)^2}=\sqrt{1 + 16}=\sqrt{17}$.

Step4: Approximate to nearest hundredth

$\sqrt{17}\approx4.12$.

Answer:

$4.12$