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in Straight Lines by (56.4k points)

If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

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Let A (x1, y1), B (x2, y2) and C (x3, y3) be the vertices of triangle ABC.

Let D (-2, 3), E (4, -3) and F (4, 5) be the mid-points of sides BC, CA and AB respectively.

As D is the mid-point of BC

Similarly E and F are the mid-points of AC and AB

Thus, the coordinates of C are (-2, -5)

Hence, the vertices of triangle ABC are A (10, -1), B (-2, 11) and C (-2, -5).

Therefore, the coordinates of the centroid of triangle ABC are

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