Question

what is the distance between the points (3,6) and (-15,-18) in the coordinate plane?
a. 18
b. 24
c. 20
d. 30

Explanation:

Step1: Identify the 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, \(x_1 = 3,y_1=6,x_2=-15,y_2 = - 18\).

Step2: Calculate \(x_2 - x_1\) and \(y_2 - y_1\)

\(x_2 - x_1=-15 - 3=-18\), \(y_2 - y_1=-18 - 6=-24\)

Step3: Square the differences

\((x_2 - x_1)^2=(-18)^2 = 324\), \((y_2 - y_1)^2=(-24)^2=576\)

Step4: Sum the squares

\((x_2 - x_1)^2+(y_2 - y_1)^2=324 + 576=900\)

Step5: Take the square - root

\(d=\sqrt{900}=30\)

Answer:

D. 30