Question

the midpoint formula is...
(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})
the distance formula is...
d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

1. cooper and abby want to see how far apart they lived from one another. they created a map with a grid

where each unit represents 1 mile. they marked abby at (10,2) and cooper at (4,4).
a. to the nearest miles, how far apart are they?

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(4,4)\) and \((x_2,y_2)=(10,2)\)

Step2: Substitute into the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute \(x_1 = 4,x_2=10,y_1 = 4,y_2 = 2\)
\(d=\sqrt{(10 - 4)^2+(2 - 4)^2}\)

Step3: Calculate the squares

\((10 - 4)^2=6^2 = 36\) and \((2 - 4)^2=(- 2)^2=4\)
\(d=\sqrt{36 + 4}\)

Step4: Sum and find the square - root

\(36+4 = 40\), so \(d=\sqrt{40}\)
\(\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}\approx2\times3.162 = 6.324\approx6\)

Answer:

\(6\)