Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-5,5) and (4, -7)

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, \(x_1=-5,y_1 = 5,x_2 = 4,y_2=-7\).

Step2: Substitute values into formula

First, calculate \(x_2 - x_1=4-(-5)=4 + 5=9\) and \(y_2 - y_1=-7 - 5=-12\). Then, substitute these into the formula: \(d=\sqrt{(9)^2+(-12)^2}\).

Step3: Simplify the expression

Calculate \((9)^2 = 81\) and \((-12)^2=144\). Then, \(81 + 144=225\). So, \(d=\sqrt{225}\). Wait, no, wait, \(9^2+(-12)^2=81 + 144 = 225\)? Wait, no, \(9^2=81\), \((-12)^2 = 144\), \(81+144 = 225\), and \(\sqrt{225}=15\)? Wait, that's a whole number. Wait, let's check again. \(x_2 - x_1=4-(-5)=9\), \(y_2 - y_1=-7 - 5=-12\). Then \((x_2 - x_1)^2=81\), \((y_2 - y_1)^2 = 144\). Sum is \(81 + 144=225\), square root of 225 is 15. So the distance is 15.0 (since we can write it to the nearest tenth, but 15 is a whole number, so 15.0 or just 15).

Answer:

15.0