Question

3 points lie on an xy plane, with each point representing where a particular person lives. Amy lives at point (2,3); Brian lives at point (0,7); and Claire lives at point (-2,3). They all wish to meet up with each other for lunch, but at a location that is equidistant from each of their respective houses. At what point do they meet?

Answer 1

The equidistant point for all three, will be the "centroid" of their triangular locations
thus $\bf \textit{Centroid of a Triangle} \begin{array}{llll} Amy \begin{array}{llll} (2,3)\\ x_1,y_1 \end{array}\quad Brian \begin{array}{llll} (0,7)\\ x_2,y_2 \end{array}\quad Claire \begin{array}{llll} (-2,3)\\ x_3,y_3 \end{array}\\ \quad \\\\\\ \left(\cfrac{x_1+x_2+x_3}{3}\quad ,\cfrac{y_1+y_2+y_3}{3}\quad \right) \end{array}$