Question

find the distance between the two points rounding to the nearest tenth (if necessary). (1, -3) and (-7, 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, \(x_1 = 1\), \(y_1=-3\), \(x_2=-7\), \(y_2 = 2\).

Step2: Substitute values into formula

First, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=-7 - 1=-8\)
\(y_2 - y_1=2-(-3)=2 + 3 = 5\)

Then, substitute into the distance formula:
\(d=\sqrt{(-8)^2+5^2}=\sqrt{64 + 25}=\sqrt{89}\)

Step3: Calculate and round

\(\sqrt{89}\approx9.43398\), rounding to the nearest tenth gives \(9.4\).

Answer:

\(9.4\)