A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of the vertices of the park are (1, 1), (1, 4), and (−3, 4). The city planner wants to put recycling bins at the circumcenter of the park. What are the coordinates of the recycling bins?

The area of the triangle enclosed by the three points

A(1,1), B(1,4) and C(-3,4) in this question will be given by

|Ax ( By − Cy)+ Bx(Cy−Ay)+ Cx(Ay− By) |/2

=|1(4-4)+1(4-1)+-3(1-4)|/2=10/5= 5 sq. units

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