Question

find the distance between the points (2, 1) and (9, 7). round decimals to the nearest tenth. units

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, \(x_1 = 2\), \(y_1 = 1\), \(x_2 = 9\), \(y_2 = 7\).

Step2: Substitute values into formula

First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
\(x_2 - x_1=9 - 2 = 7\)
\(y_2 - y_1=7 - 1 = 6\)
Then, substitute into the formula:
\(d=\sqrt{(7)^2+(6)^2}=\sqrt{49 + 36}=\sqrt{85}\)

Step3: Calculate and round

\(\sqrt{85}\approx9.2195\), rounding to the nearest tenth gives \(9.2\).

Answer:

\(9.2\)