Question

MODELING REAL LIFE The coordinate plane shows dig sites for archaeological research. Each unit on the grid represents 1 square foot. What is the distance from Site A to Site C? y 30 25 Site A Site B 20 15 10 5 Site Y 10 15 20 The distance is feet.

Answer 1

The coordinates of site A are (5,20) and the coordinates of site C are (25,5).

The distance between two points is given by:

$d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

Then, in this case we have:

$\begin{gathered} d(A,C)=\sqrt[]{(25-5)^2+(5-20)^2} \\ =\sqrt[]{20^2+(-15)^2} \\ =\sqrt[]{400+225} \\ =\sqrt[]{625} \\ =25 \end{gathered}$

Therefore the distance between sites A and B is 25 ft.