Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-6, -4) and (0, 2)

Explanation:

Step1: Recall distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Here, \(x_1=-6,y_1 = - 4,x_2 = 0,y_2=2\).

Step2: Substitute values into formula

Substitute the values into the formula:
\(d=\sqrt{(0 - (-6))^2+(2 - (-4))^2}=\sqrt{(6)^2+(6)^2}\)

Step3: Simplify the expression

First, calculate the squares: \(6^2 = 36\), so we have \(\sqrt{36 + 36}=\sqrt{72}\)

Step4: Simplify \(\sqrt{72}\) and round

\(\sqrt{72}\approx8.485\), rounding to the nearest tenth gives \(8.5\)

Answer:

\(8.5\)