Question

While creating a map Louis used a grid system. Louis determined that a mountain could be given the coordinates (500,1259) and that his current position could be given by the coordinates (250,129). If a pond is located exactly halfway between Louis and the mountain, what coordinates should Louis use to represent the pond's location?

Answer 1

Since the pond is located exactly halfway between Louis and the mountain, then to find its coordinates, you can use the formula to determine the midpoint of a segment

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

In this case, you have

$\begin{gathered} (x_1,y_1)=(500,1259) \\ (x_2,y_2)=\mleft(250,129\mright) \end{gathered}$$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{500+250}{2},\frac{1259+129}{2})=(\frac{750}{2},\frac{1388}{2})=(375,694)$$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(375,694)$

Therefore, the coordinates Louis should use to represent the location of the pond are (375,694).