Question

Davis Construction is building a new housing development. They begin by mapping the development out on a coordinate grid. They place one of the two swimming pools at (-8, -7) and the other at (10, 15). If they want the clubhouse to be exactly halfway between the two pools, find the coordinates for the clubhouse.

Answer 1

${\text{Davis Construction is building a new housing development}}{\text{. They begin by mapping }} \hfill \\ {\text{the development out on a coordinate grid}}{\text{.}} \hfill \\ {\text{They place one of the two swimming pools at A}}\left( { - 8,{\text{ }} - 7} \right){\text{ and the other}} \hfill \\ {\text{at B}}\left( {10,{\text{ }}15} \right).{\text{ They want the clubhouse to be exactly}} \hfill \\ {\text{halfway between the two pools}}. {\text{ The coordinates of clubhouse can }} \hfill \\ x = \frac{{{x_1} + {x_2}}}{2},y = \frac{{{y_1} + {y_2}}}{2} \hfill \\ {\text{On substituting the coordinates of two swimming pools located at }} \hfill \\ {\text{A}}\left( { - 8,{\text{ }} - 7} \right){\text{ and B}}\left( {10,{\text{ }}15} \right){\text{ in the above formula, we get coordinates of c}}\operatorname{lub} {\text{house as}} \hfill \\ x = \frac{{ - 8 + 10}}{2} = \frac{2}{2} = 1,y = \frac{{ - 7 + 15}}{2} = \frac{8}{2} = 4 \hfill \\{\text{Thus, the coordinates of clubhouse on the grid paper is }}\left( {1,4} \right). \hfill$