Question

A construction crew plans to build a new stadium in the center of the three towns shown on this coordinate map. What are the coordinates of the point where the new stadium will be built?

o (1, 1)
O
O
(3, 4)

Answer 1

(b) (1, 4/3)

Explanation:

You want the coordinates of the "center" of the three towns at coordinates (-4, 3), (6, 3) and (1, -2) on the map.

Center

A number of centers are described for a triangle:

• circumcenter
• incenter
• orthocenter
• center of gravity

While the circumcenter would be equidistant from the three towns, that is not an available option. Apparently, the center intended is the center of gravity, the intersection of medians of the triangle. It can be computed as the average of the coordinates of the three towns.

((-4, 3) +(6, 3) +(1, -2))/3 = (-4+6+1, 3+3-2)/3 = (3, 4)/3 = (1, 4/3)

The coordinates of the stadium are (1, 4/3).