Discussion
Find the coordinates of the circumcenter of the triangle whose vertices are (8, 6), (8, -2) and (2, -2).
Answer: A
First, notice the vertices. The side from (8, 6) to (8, -2) is a vertical line (x=8). The side from (8, -2) to (2, -2) is a horizontal line (y=-2). This means they are perpendicular, and the triangle is a right-angled triangle with the right angle at (8, -2).
In a right-angled triangle, the circumcenter is the midpoint of the hypotenuse.
The hypotenuse connects the vertices (8, 6) and (2, -2).
Midpoint = \((\frac{8+2}{2}, \frac{6+(-2)}{2}) = (\frac{10}{2}, \frac{4}{2}) = (5, 2)\).
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