Question

find the distance between the points (-9, -4) and (-7, 8). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify the distance - formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-9,y_1 = - 4,x_2=-7,y_2 = 8\).

Step2: Calculate the differences

First, find \(x_2 - x_1\) and \(y_2 - y_1\).
\(x_2 - x_1=-7-(-9)=-7 + 9=2\)
\(y_2 - y_1=8-(-4)=8 + 4 = 12\)

Step3: Substitute into the formula

Substitute the values into the distance formula:
\(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{2^2+12^2}=\sqrt{4 + 144}=\sqrt{148}\)

Step4: Simplify the radical

Factor 148: \(148=4\times37\), so \(\sqrt{148}=\sqrt{4\times37}=2\sqrt{37}\)

Answer:

\(2\sqrt{37}\)