Question

find the distance between the points (7,2) and (-3,-5).
the distance between the two given points is
(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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Identify coordinates

Let $(x_1,y_1)=(7,2)$ and $(x_2,y_2)=(-3,-5)$.

Step3: Substitute values

$d=\sqrt{(-3 - 7)^2+(-5 - 2)^2}=\sqrt{(-10)^2+(-7)^2}$.

Step4: Calculate squares

$d=\sqrt{100 + 49}=\sqrt{149}$.

Answer:

$\sqrt{149}$