Question

Find the circumcenter of the triangle with E(4, 4), F(4, 2), and G(8, 2). Hint: Draw a sketch of the triangle with the point locations.

a) (6, 3)
b) (5, 4)
c) (6, 4)
d) (4, 3)

Answer 1

The circumcenter of the triangle with vertices E(4, 4), F(4, 2), and G(8, 2) is found at the intersection of the perpendicular bisectors of sides EF and FG, which is the point (6, 3).

Step-by-step explanation:

The question involves finding the circumcenter of a triangle in a coordinate plane. The points of the triangle are E(4, 4), F(4, 2), and G(8, 2). To find the circumcenter, you must find the point where the perpendicular bisectors of the sides of the triangle intersect. Since points E and F have the same x-coordinate, the perpendicular bisector of side EF is a horizontal line with an equation that has a y-coordinate midway between the y-coordinates of E and F, which is y = 3.

Since points F and G have the same y-coordinate, the perpendicular bisector of side FG is a vertical line that also passes through the midpoint of FG, with an x-coordinate that is the average of the x-coordinates of F and G, which is x = 6. Therefore, the circumcenter is at the intersection of these two perpendicular bisectors, which is at (6, 3).