Quiz 5-2 Centers Of Triangles Answer Key Jun 2026

P(0,0), Q(4,0), R(1,3). Perpendicular bisector of PQ: x=2. Perpendicular bisector of PR: Midpoint (0.5,1.5). Slope PR = 3/1=3 → perp slope = -1/3. Equation: y-1.5 = (-1/3)(x-0.5). Set x=2 → y-1.5 = (-1/3)(1.5) = -0.5 → y = 1.0. Circumcenter = (2,1) – outside triangle? Check: Yes, it’s to the right of R.

If G is the centroid of triangle ABC, and AG = 8, find the length of the median from A. 12. Explanation: Centroid divides median in ratio 2:1 (vertex to centroid : centroid to midpoint). So AG = 2/3 of median → 8 = (2/3)×median → median = 12. quiz 5-2 centers of triangles answer key

Below are the common types of problems found in Quiz 5-2 with their detailed step-by-step solutions: The centroid ( ) divides each median into two segments: one is P(0,0), Q(4,0), R(1,3)

Here is a refresher on the four vital points: Slope PR = 3/1=3 → perp slope = -1/3