Question

find the distance between the points given below. give the exact answer as a simplified radical, if necessary.
(4,3),(-8,-6)
answer 2 points
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Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(4,3)\) and \((x_2,y_2)=(-8,-6)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(x_2 - x_1=-8 - 4=-12\), \(y_2 - y_1=-6 - 3=-9\)

Step3: Calculate \((x_2 - x_1)^2\) and \((y_2 - y_1)^2\)

\((x_2 - x_1)^2=(-12)^2 = 144\), \((y_2 - y_1)^2=(-9)^2=81\)

Step4: Sum the results and take the square - root

\(d=\sqrt{144 + 81}=\sqrt{225}\)

Answer:

\(15\)