Question in description

Question

1) A hospital is to be built to serve 3 surrounding cities. Flagflog is located at (-40, 70) on a map, Herbert is located at (10, 80) and City is located at (-20, 50). Where should the hospital be built so that all the cities are the same distance away from the hospital.

2) A metallic triangle has vertices defined by (-5, 7), (2,5,) and (-1, -3). For some reason, I want to balance this triangle on a pin(I guess I want to impress someone). Where should I place the pin so that it balances perfectly (find the centre of mass!)?

I need all the steps, they are marked out of 10.Thanks SO much.

Answer 1

1) determine the circumcenter, the intersection of the perpendicular bisectors of the three sides.

2) determine the orthocenter, the intersection of the medians of the three sides.