Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-5, 4) and (4, -8)

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, \(x_1=- 5,y_1 = 4,x_2=4,y_2=-8\).

Step2: Substitute the values into the formula

First, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=4-(-5)=4 + 5=9\)
\(y_2 - y_1=-8 - 4=-12\)
Then, substitute these into the distance formula:
\(d=\sqrt{(9)^2+(-12)^2}=\sqrt{81 + 144}=\sqrt{225}\) (Wait, no, \(81+144 = 225\)? Wait, \(81+144=225\)? Wait, \(9^2=81\), \((- 12)^2 = 144\), \(81 + 144=225\), but \(\sqrt{225}=15\)? Wait, no, wait, \(9^2+(-12)^2=81 + 144 = 225\), so \(\sqrt{225}=15\). Wait, but let's check again. Wait, \(x_1=-5,x_2 = 4\), so \(x_2 - x_1=4-(-5)=9\), correct. \(y_1 = 4,y_2=-8\), so \(y_2 - y_1=-8 - 4=-12\), correct. Then \((9)^2=81\), \((-12)^2 = 144\), sum is \(81 + 144=225\), square root of \(225\) is \(15\). So the distance is \(15.0\) when rounded to the nearest tenth.

Wait, maybe I made a mistake earlier. Wait, \(81+144 = 225\), square root of \(225\) is \(15\), so the distance is \(15.0\).

Answer:

\(15.0\)