Question

Two vertices of a triangle are (−5, 3) and (4, −7). If centroid of the triangle is (−1, 2) then the third vertex is ______.

Options

• (−2, 7)

• (−2, 10)

• (−2, −10)

• (0, −2)

Answer 1

Two vertices of a triangle are (−5, 3) and (4, −7). If centroid of the triangle is (−1, 2) then the third vertex is (−2, 10).

Explanation:

Let third vertex be \[(x, y).\]

By formula,

Centroid of triangle \[{} = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right)\]

Substituting values we get:

⇒ \[(-1, 2) = \left(\frac{(-5) + 4 + x}{3}, \frac{3 + (-7) + y}{3}\right)\]

⇒ \[(-1, 2) = \left(\frac{x - 1}{3}, \frac{y - 4}{3}\right)\]

⇒ \[-1 = \frac{x - 1}{3}\] and \[2 = \frac{y - 4}{3}\]

⇒ \[x - 1 = -3\] and \[y - 4 = 6\]

⇒ \[x = -3 + 1\] and \[y = 6 + 4\]

⇒ \[x = -2\] and \[y = 10.\]

Third vertex \[{} = (-2, 10).\]