If two vertices of a triangle are (6,4), (2,6) and its centroid is (4, 6), then

Question

If two vertices of a triangle are (6,4), (2,6) and its centroid is (4, 6), then the third vertex is

Options:

A . (4,8)

B . (8,4)

C . (6,4)

D . (0,0)

Answer: Option A
:
A
Given:
Centroid =

(4, 6)

Vertices

(6, 4) & (2, 6)

Let the Co-ordinates of

C

(x_{3}, y_{3})

x_{1} = 6, x_{2} = 32, y_{1} = 4 & y_{2} = 6

Centroid

(4, 6) = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})

\Rightarrow 4 = \frac{6 + 2 + x_{3}}{3}

and

6 = \frac{4 + 6 + y_{3}}{3}

\Rightarrow

x_{3} = 4

and

y_{3} = 8

∴

Third vertex is

(4, 8)

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