Question

Find the coordinates of the circumcenter of the triangle with the given vertices.

2. R(-2,5), S(-6, 5), T(-2,-1)​

Answer 1

(-4, 2)

Explanation:

You want the circumcenter of the triangle with vertices R(-2, 5), S(-6, 5), T(-2, -1).

Triangle

A plot of the points reveals the triangle to be a right triangle. (We know that because two points have the same x-coordinate, and two points have the same y-coordinate, meaning the sides are grid-aligned and at right angles.)

Circumcenter

The point R is the right-angle corner, so side ST is the hypotenuse. Its midpoint is the circumcenter of the triangle.

C = (S +T)/2

C = ((-6, 5) +(-2, -1))/2 = (-6-2, 5-1)/2 = (-4, 2)

The circumcenter of the triangle is (-4, 2).

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