Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-7,9) and (-2,6)

Explanation:

Step1: Recall the 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, \(x_1=-7\), \(y_1 = 9\), \(x_2=-2\), \(y_2=6\).

Step2: Substitute the values into the formula

First, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=-2-(-7)=-2 + 7 = 5\)
\(y_2 - y_1=6 - 9=-3\)
Then, substitute these into the distance formula:
\(d=\sqrt{(5)^2+(-3)^2}=\sqrt{25 + 9}=\sqrt{34}\)

Step3: Approximate \(\sqrt{34}\) to the nearest tenth

We know that \(\sqrt{34}\approx5.83095\). Rounding to the nearest tenth, we look at the hundredth place. The digit in the hundredth place is 3, which is less than 5, so we round down. So \(\sqrt{34}\approx5.8\).

Answer:

\(5.8\)