Question

table of contents > lesson 4: graph equations in two variables > graded activities > lesson 4 homework
lesson 4 homework
use the distance formula, given two points
question
find the distance between the points (-2,6) and (7,3).
give an exact answer in simplest radical form. do not round.
provide your answer below.

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 $(x_1,y_1)=(-2,6)$ and $(x_2,y_2)=(7,3)$. Then $x_1=-2,y_1 = 6,x_2=7,y_2 = 3$.

Step3: Substitute values into the formula

$d=\sqrt{(7-(-2))^2+(3 - 6)^2}=\sqrt{(7 + 2)^2+(3 - 6)^2}=\sqrt{9^2+(-3)^2}$.

Step4: Calculate the squares

$\sqrt{9^2+(-3)^2}=\sqrt{81 + 9}$.

Step5: Simplify the sum under the square - root

$\sqrt{81+9}=\sqrt{90}$.

Step6: Simplify the radical

$\sqrt{90}=\sqrt{9\times10}=3\sqrt{10}$.

Answer:

$3\sqrt{10}$