The centroid of a triangle is given as C(a,3b) having vertices A(-a,2b), B(-2a,4b) and C(x,y).the values of x and y are

6a and 6b

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3a and 3b

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3a and 6b

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6a and 3b

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Solution

The correct option is D 6a and 3b
Given that,
Point A (-a,2b), B(-2a,4b)
Centroid C(a,3b)
Centroid $= (\frac{(x_{1} + x_{2} + x_{3})}{3} + \frac{(y_{1} + y_{2} + y_{3})}{3}) (a, 3 b) = (\frac{(- a - 2 a + x)}{3}, (\frac{2 b + 4 b + y}{3})) (a, 3 b) = ((\frac{- 3 a + x}{3}), (\frac{6 b + y}{3})) E q u a t i n g c o r r e s p o n d i n g C o o r d i n a t e s, a = \frac{- 3 a + x}{3} \Rightarrow 6 a = x b = \frac{6 b + y}{3} \Rightarrow 3 b = y H e n c e O p t i o n A i s t h e c o r r e c t a n s w e r$

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The centroid of a triangle is given as C(a,3b) having vertices A(-a,2b), B(-2a,4b) and C(x,y).the values of x and y are

The correct option is D 6a and 3bGiven that, Point A (-a,2b), B(-2a,4b) Centroid C(a,3b) Centroid =((x1+x2+x3)3+(y1+y2+y3)3)(a,3b) =((−a−2a+x)3,(2b+4b+y3))(a,3b) = ((−3a+x3),(6b+y3))Equating corresponding Co ordinates,a=−3a+x3⇒6a=xb=6b+y3⇒3b=yHence Option A is the correct answer