Question

Find the coordinates of the centroid of the triangle with the given vertices. (Lesson 5-2)

Answer 1

The triangle with vertices located at A(1 , 7), B(4 , 2), and C(7 , 7) has its centroid located at (4 , 16/3).

The centroid of a triangle is the point inside the triangle where the three medians intersect. The median of a triangle is the line the connects the midpoint of a side and the opposite vertex.

To get the centroid of a triangle, use the formula given by:

C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]

where C is the centroid of the triangle located at (x , y)

x1, x2, and x3 are the x-coordinate of the vertices of the triangle

y1, y2, and y3 are the y-coordinate of the vertices of the triangle

Let Point 1(x1 , y1) =  A(1 , 7)

Point 2(x2 , y2) = B(4 , 2)

Point 3(x3 , y3) = C(7 , 7)

Plug in the values in the formula.

C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]

C(x ,y) = [(1 +4 + 7)/3 , (7 + 2 + 7)/3]

C(x ,y) = (12/3 , 16/3)

C(x ,y) = (4 , 16/3)

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