If the centroid of the triangle formed by (7, x)
Question:

If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =

(a) (4, 5)

(b) (5, 4)

(c) (−5, −2)

(d) (5, 2)

Solution:

We have to find the unknown co-ordinates.

The co-ordinates of vertices are $\mathrm{A}(7, x) ; \mathrm{B}(y,-6) ; \mathrm{C}(9,10)$

The co-ordinate of the centroid is (6, 3)

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,

$(6,3)=\left(\frac{y+7+9}{3}, \frac{x-6+10}{3}\right)$

Compare individual terms on both the sides-

$\frac{x+4}{3}=3$

So,

$x=5$

Similarly,

$\frac{y+16}{3}=6$

So,

$y=2$

So the answer is (d)

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