Question

find the distance between the points (7, 8) and (-3, 4). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify 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 $(x_1,y_1)=(7,8)$ and $(x_2,y_2)=(-3,4)$. Then $d=\sqrt{(-3 - 7)^2+(4 - 8)^2}$.

Step3: Simplify the expressions inside the square - root

First, $-3-7=-10$ and $4 - 8=-4$. So $d=\sqrt{(-10)^2+(-4)^2}=\sqrt{100 + 16}$.

Step4: Calculate the sum inside the square - root

$100+16 = 116$, so $d=\sqrt{116}$.

Step5: Simplify the radical

$116=4\times29$, so $\sqrt{116}=\sqrt{4\times29}=2\sqrt{29}$.

Answer:

$2\sqrt{29}$