Question

find the distance between the points (-4, -3) and (-3, 9). write your answer as a whole number or a fully simplified radical expression. do not round.

units

Explanation:

Step1: Recall distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Here, \(x_1=-4,y_1 = - 3,x_2=-3,y_2 = 9\).

Step2: Substitute values into formula

First, calculate \(x_2 - x_1=-3-(-4)=-3 + 4 = 1\).
Then, calculate \(y_2 - y_1=9-(-3)=9 + 3 = 12\).
Now, substitute these into the distance formula: \(d=\sqrt{(1)^2+(12)^2}\).

Step3: Simplify the expression

Calculate \((1)^2 = 1\) and \((12)^2=144\). Then \(1 + 144=145\). So \(d=\sqrt{145}\).

Answer:

\(\sqrt{145}\)