Question

find the distance between the points (6, 7) and (10, 3). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 6,y_1 = 7,x_2=10,y_2 = 3$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=10 - 6=4$ and $y_2 - y_1=3 - 7=- 4$.

Step3: Square the differences

$(x_2 - x_1)^2=4^2 = 16$ and $(y_2 - y_1)^2=(-4)^2 = 16$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=16 + 16=32$.

Step5: Take the square - root

$d=\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$ units.

Answer:

$4\sqrt{2}$ units