Question

find the distance between the pair of points (-3, -4) and (5, -3). if necessary, express the answer in simplified radical form and then round to two decimal places.
the distance between the given points is units. (simplify your answer. type an exact answer using radicals as needed.)

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, $x_1=-3,y_1 = - 4,x_2=5,y_2=-3$.

Step2: Substitute values

$d=\sqrt{(5-(-3))^2+((-3)-(-4))^2}=\sqrt{(5 + 3)^2+(-3 + 4)^2}=\sqrt{8^2+1^2}=\sqrt{64 + 1}=\sqrt{65}$.

Step3: Round to two - decimal places

$\sqrt{65}\approx 8.06$.

Answer:

$\sqrt{65}\approx8.06$