Question

find the distance between the points (7, 5) and (4, 8). 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: Assign values

Let $(x_1,y_1)=(7,5)$ and $(x_2,y_2)=(4,8)$. Then $x_2 - x_1=4 - 7=-3$ and $y_2 - y_1=8 - 5 = 3$.

Step3: Calculate squares and sum

$(x_2 - x_1)^2=(-3)^2 = 9$ and $(y_2 - y_1)^2=3^2 = 9$. The sum is $9+9 = 18$.

Step4: Find distance

$d=\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$.

Answer:

$3\sqrt{2}$ units