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

`((x_1+x_2)/(2),(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}`
`((x_1+x_2)/(2),(y_1+y_2)/(2))=((500+250)/(2),(1259+129)/(2))=((750)/(2),(1388)/(2))=(375,694)`
`((x_1+x_2)/(2),(y_1+y_2)/(2))=(375,694)`

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