Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places. (0,0) and (12, -9) the distance between the points is units. (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(12, - 9)\)

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

Substitute the values: \(d=\sqrt{(12 - 0)^2+(-9 - 0)^2}\)

Step3: Simplify the expression inside the square - root

\((12 - 0)^2=12^2 = 144\) and \((-9 - 0)^2=(-9)^2=81\)
So \(d=\sqrt{144 + 81}\)

Step4: Add the numbers inside the square - root

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

Step5: Evaluate the square - root

\(\sqrt{225}=15\)

Answer:

\(15\)