Question

find the distance between the points (3, -5) and (7, -4). write your answer as a whole number or a fully simplified radical expression. do not round. units

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 $(x_1,y_1)=(3,-5)$ and $(x_2,y_2)=(7,-4)$. Then $x_2 - x_1=7 - 3 = 4$ and $y_2 - y_1=-4-(-5)=-4 + 5 = 1$.

Step3: Calculate the distance

$d=\sqrt{(4)^2+(1)^2}=\sqrt{16 + 1}=\sqrt{17}$.

Answer:

$\sqrt{17}$