Find the centroid of the triangle with vertices (0,0), (6,0), and (0,6).

Prepare for the Geometry CBE Exam with targeted resources. Access interactive quizzes and detailed explanations to master geometric concepts effectively and excel in your test!

Multiple Choice

Find the centroid of the triangle with vertices (0,0), (6,0), and (0,6).

The centroid is the point where a triangle’s medians intersect, and it sits at the average of the vertices’ coordinates. Take the three vertices: (0,0), (6,0), and (0,6). Average the x-coordinates: (0 + 6 + 0)/3 = 2. Average the y-coordinates: (0 + 0 + 6)/3 = 2. So the centroid is at (2, 2). This point lies inside the triangle. Other options don’t match both coordinate averages. For example, a point with y = 0 or x = 0 would not have both coordinates equal to 2, and a point like (6,6) lies far outside the triangle. The pair (2,2) satisfies both averages, so it’s the correct centroid.

The centroid is the point where a triangle’s medians intersect, and it sits at the average of the vertices’ coordinates. Take the three vertices: (0,0), (6,0), and (0,6). Average the x-coordinates: (0 + 6 + 0)/3 = 2. Average the y-coordinates: (0 + 0 + 6)/3 = 2. So the centroid is at (2, 2). This point lies inside the triangle.

Other options don’t match both coordinate averages. For example, a point with y = 0 or x = 0 would not have both coordinates equal to 2, and a point like (6,6) lies far outside the triangle. The pair (2,2) satisfies both averages, so it’s the correct centroid.

More practice questions