Question

find the distance between the points (9, 9) and (-4, -2). round decimals to the nearest tenth.

Explanation:

Step1: Identify 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, \(x_1 = 9,y_1 = 9,x_2=-4,y_2 = - 2\).

Step2: Calculate differences

First, find \(x_2 - x_1=-4 - 9=-13\) and \(y_2 - y_1=-2 - 9=-11\).

Step3: Square the differences

\((x_2 - x_1)^2=(-13)^2 = 169\) and \((y_2 - y_1)^2=(-11)^2 = 121\).

Step4: Sum the squared - differences

\((x_2 - x_1)^2+(y_2 - y_1)^2=169 + 121=290\).

Step5: Calculate the square - root

\(d=\sqrt{290}\approx17.0\) (rounded to the nearest tenth).

Answer:

17.0