Question

lesson 4 homework
use the distance formula, given two points
question
find the distance between the points (-1, 7) and (9, 5).
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 values to variables

Let $(x_1,y_1)=(-1,7)$ and $(x_2,y_2)=(9,5)$. Then $x_2 - x_1=9-(-1)=10$ and $y_2 - y_1=5 - 7=-2$.

Step3: Substitute into the formula

$d=\sqrt{(10)^2+(-2)^2}=\sqrt{100 + 4}=\sqrt{104}$.

Step4: Simplify the radical

$\sqrt{104}=\sqrt{4\times26}=2\sqrt{26}$.

Answer:

$2\sqrt{26}$