Question

1. two points are shown.

w (4,8), z (-8,-1)
what is the approximate distance between point w and point z?

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 4,y_1 = 8,x_2=-8,y_2=-1\).

Step2: Substitute the values into the formula

First, find \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=-8 - 4=-12\), \(y_2 - y_1=-1 - 8=-9\).
Then, \((x_2 - x_1)^2+ (y_2 - y_1)^2=(-12)^2+(-9)^2\).
\((-12)^2 = 144\), \((-9)^2=81\), so \((x_2 - x_1)^2+(y_2 - y_1)^2=144 + 81=225\).

Step3: Calculate the square - root

\(d=\sqrt{225}=15\)

Answer:

\(15\)