Question

find the distance between the points (8, 3) and (10, 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 8,y_1 = 3,x_2 = 10,y_2 = 4$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=10 - 8 = 2$ and $y_2 - y_1=4 - 3 = 1$.

Step3: Square the differences and sum

Square the results from step 2: $(x_2 - x_1)^2=2^2 = 4$ and $(y_2 - y_1)^2=1^2 = 1$. Then sum them: $(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 1=5$.

Step4: Find the distance

Take the square - root of the sum. $d=\sqrt{5}$ units.

Answer:

$\sqrt{5}$ units