Question

find the distance between the pair of points. give an exact answer, and where appropriate, an approximation to three decimal places.
(3, -6) and (12,6)
oa. 225
ob. √450, 21.213
oc. 21
od. 15

Explanation:

Step1: Use 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, \(x_1 = 3,y_1=-6,x_2 = 12,y_2 = 6\).

Step2: Substitute the values into the formula

\(d=\sqrt{(12 - 3)^2+(6-(-6))^2}=\sqrt{9^2 + 12^2}\).

Step3: Calculate the squares

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

Step4: Add the values inside the square - root

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

Step5: Simplify the square - root

\(\sqrt{225}=15\).

Answer:

D. 15