Question

7. Two vertices of a triangle are (1, 3) and (2, -4). If the origin is the
centroid of the triangle, find the third vertex.​

Answer 1

SOLUTION

GIVEN

Two vertices of a triangle are (1, 3) and (2, -4). If the origin is the centroid of the triangle

TO DETERMINE

The third vertex.

EVALUATION

Here it is given that the two vertices of a triangle are (1, 3) and (2, -4).

Let the coordinates of third vertex is (a, b)

Now origin is the centroid of the triangle

So by the given condition

$\displaystyle \sf{ \bigg( \: \frac{1 + 2 + a}{3} \:, \: \frac{3 - 4 + b}{3} \bigg) = (0 , 0)}$

$\displaystyle \sf{ \implies \: \bigg( \: \frac{a + 3}{3} \:, \: \frac{ b - 1}{3} \bigg) = (0 , 0)}$

$\displaystyle \sf{ \implies \: \frac{a + 3}{3} = 0 \:, \: \frac{ b - 1}{3} = 0}$

$\displaystyle \sf{ \implies \: a + 3= 0 \:, \: b - 1= 0}$

$\displaystyle \sf{ \implies \: a = - 3 \:, \: b = 1}$

Hence the required third vertex = ( - 3 , 1 )

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