Question

If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6),
Q(-4, 36,-10) and R(8, 14, 2c), then find the values of a, b and c.​

Answer 1

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Answer 2

Centroid of the triangle is the point of intersection of medians of the triangle.

Given, Origin is the centroid of the triangle PQR.

So, G = ( 0, 0, 0)

Vertices of the triangle are,

P (2a, 2, 6)

Q(-4, 3b,-10)

R(8, 14, 2c)

Centroid of the triangle is given by,

$= ( \frac{2a - 4 + 8}{3} \frac{2 + 3b + 14}{3} \frac{6 - 10 + 2c}{3} )$

So,

Comparing X coordinate

$\frac{2a - 4 + 8}{3} = 0 \\ \\ 2a + 4 = 0 \\ \\ 2a = - 4 \\ \\ a = \frac{ - 4}{2} = - 2$

Comparing Y coordinate

$\frac{2 + 3b + 14}{3} = 0 \\ \\ 3b + 16 = 0 \\ \\ 3b = - 16 \\ \\ b = \frac{ - 16}{3}$

Comparing Z coordinate

$\frac{6 - 10 + 2c}{3} = 0 \\ \\ - 4 + 2c = 0 \\ \\ 2c = 4 \\ \\ c = \frac{4}{2 } \\ \\ c = 2$

Therefore, a = - 2 , b =-16/3 , c = 2