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 coordinate (-16, -25) and the other at (18, 23). If they want the club house to be exactly halfway between the two pools, find the coordinate point for the clubhouse

Answer 1

To solve this problem, we can use the following ratio formulas to find for the coordinates of the club house:

x = [m / (m + n)] (x2 – x1) + x1

y = [m / (m + n)] (y2 – y1) + y1

Where,

m and n are the ratios (0.5 and 0.5 each since the club house are to be located exactly halfway)

x1 and y1 are the x and y coordinates of the 1st pool (-16, -25)

x2 and y2 are the x and y coordinates of the 2nd pool (18, 23)

Substituting:

x = [0.5 / (0.5 + 0.5)] (18 - -16) + -16

x = 1

y = [0.5 / (0.5 + 0.5)] (23 - -25) + -25

y = -1

Therefore the club house should be located at coordinates (1, -1).