Question

find the distance between the points (-1, 7) and (4, 6). write your answer as a whole number or a fully simplified radical expression. do not round.

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: Substitute the given points

Let $(x_1,y_1)=(-1,7)$ and $(x_2,y_2)=(4,6)$. Then $x_2 - x_1=4-(-1)=5$ and $y_2 - y_1=6 - 7=-1$.

Step3: Calculate the distance

$d=\sqrt{(5)^2+(-1)^2}=\sqrt{25 + 1}=\sqrt{26}$.

Answer:

$\sqrt{26}$