Question

lesson 4 homework use the distance formula, given two points question find the distance between the points (-10,7) and (2,5). give an exact answer in simplest radical form. do not round provide your answer below d = □

Explanation:

Step1: Identify the 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: Assign the values of the points

Let $(x_1,y_1)=(-10,7)$ and $(x_2,y_2)=(2,5)$. Then $x_2 - x_1=2-(-10)=12$ and $y_2 - y_1=5 - 7=-2$.

Step3: Substitute into the formula

$d=\sqrt{(12)^2+(-2)^2}=\sqrt{144 + 4}=\sqrt{148}$.

Step4: Simplify the radical

$\sqrt{148}=\sqrt{4\times37}=2\sqrt{37}$.

Answer:

$2\sqrt{37}$