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Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex - Mathematics

Sum

Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex

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Solution

Let the coordinates of the third vertex be (x, y). Then,

`\frac{x+3-7}{3}=2\text{ and }\frac{y-5+4}{3}=-1`

⇒ x – 4 = 6 and y – 1 = – 3

⇒ x = 10 and y = – 2

Thus, the coordinates of the third vertex are (10, –2).

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