Question

section 1.3 distance formula
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grade: 17%
due: october 1 at 8:00 am
answer
attempt 1 out of 2
find the distance between the two points in simplest radical form.

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: Assume the coordinates

Let the lower - left point be $(x_1,y_1)$ and the upper - right point be $(x_2,y_2)$. From the graph, assume the lower - left point is $(0, - 8)$ and the upper - right point is $(4,2)$.

Step3: Substitute into the formula

$d=\sqrt{(4 - 0)^2+(2-(-8))^2}=\sqrt{4^2+(2 + 8)^2}=\sqrt{16 + 100}=\sqrt{116}$.

Step4: Simplify the radical

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

Answer:

$2\sqrt{29}$