If (−2, 1) is the centroid of the triangle having its vertices at

Question:

If (−2, 1) is the centroid of the triangle having its vertices at (x , 0) (5, −2),  (−8, y), then xy satisfy the relation

(a) 3x + 8y = 0

(b) 3x − 8y = 0

(c) 8x + 3y = 0

(d) 8x = 3y

Solution:

We have to find the unknown co-ordinates.

The co-ordinates of vertices are $\mathrm{A}(x, 0) ; \mathrm{B}(5,-2) ; \mathrm{C}(-8, y)$

The co-ordinate of the centroid is (−2, 1)

We know that the co-ordinates of the centroid of a triangle whose vertices are $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right)$ is-

$\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$

So,

$(-2,1)=\left(\frac{x+5-8}{3}, \frac{y-2}{3}\right)$

Compare individual terms on both the sides-

$\frac{x-3}{3}=-2$

So,

$x=-3$

Similarly,

$\frac{y-2}{3}=1$

So,

$y=5$

It can be observed that (xy) = (−3, 5) does not satisfy any of the relations 3x + 8y = 0, 3x − 8y = 0, 8x + 3y = 0 or 8x = 3y.

 

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