Question

. Find the value of (x, y), if centroid of the triangle with vertices (x, 0), (0, y) and (6, 3) is (3,4). (a) (3,0) (b) (6,6) () (3,9) (d) (-6,8)​

Answer 1

Answer:

please refer the attached photo*

answer-option(C)...as solved in the attached photo....

hope it helps:)

Answer 2

Given,

Vertices of triangle $\[ = \left( {x,0} \right),\left( {0,y} \right),\left( {6,3} \right)\]$

Centroid of triangle $\[ = \left( {3,4} \right)\]$

Solution,

Consider the vertices of triangle are $\[\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right),\left( {{x_3},{y_3}} \right)\]$

The centroid of triangle is $\[\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3}} \right)\]$

$\[\left( {3,4} \right) = \left( {\frac{{x + 0 + 6}}{3},\frac{{0 + y + 3}}{3}} \right)\]$

$\[\left( {3,4} \right) = \left( {\frac{{x + 6}}{3},\frac{{y + 3}}{3}} \right)\]$

$\[\begin{array}{l}\frac{{x + 6}}{3} = 3\\ \Rightarrow x + 6 = 9\\ \Rightarrow x = 3\end{array}\]$

$\[\begin{array}{l}\frac{{y + 3}}{3} = 4\\ \Rightarrow y + 3 = 12\\ \Rightarrow y = 9\end{array}\]$

$\[\left( {x,y} \right) = \left( {3,9} \right)\]$

Hence the value of $\[\left( {x,y} \right)\]$ is $\[\left( {3,9} \right)\]$

The correct option is (c), i.e. $\[\left( {3,9} \right)\]$