If $G\left( {1,\;4} \right)$ is the centroid of triangle $ABC$ having its two vertices $A$ and $B$ at $\left( {4, - 3} \right)$ and $\left( { - 9,\;7} \right)$ respectively, then area of the triangle $ABC$ in square units, is

JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

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Application +4 | -1

G\left( {1,\;4} \right)

is the centroid of triangle

ABC

having its two vertices

A

and

B

\left( {4, - 3} \right)

and

\left( { - 9,\;7} \right)

respectively, then area of the triangle

ABC

in square units, is

View answer and explanation

Correct option: C

\frac{{183}}{2}

Option C (

\frac{{183}}{{2}}

) is correct because the area of triangle ABC is three times the area of triangle GAB, where G is the centroid.

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\left( { - 10,\;8} \right)

\left( { - 6,\;12} \right)

\left( {4,\; - 2} \right)

\left( { - 2,\;4} \right)

y z

(1,-2,4)

(3,-4

5)

p

2 x+y-3=0

3 x-y-2=0

x-p y+5=0

O\left( {0,0} \right),A\left( {a,0} \right)

B\left( {0,a} \right).

A(1,0,3)

B(4,7,1)

C(3,5,3)

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}, \frac{x}{2}=\frac{y}{1}=\frac{z}{3}

\frac{x-1}{1}=\frac{2-y}{2}, z=3