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Let ABC be an acute- angled triangle and...

Let ABC be an acute- angled triangle and AD, BE, and CF be its medians, where E and F are at (3,4) and (1,2) respectively. The centroid of `DeltaABC` `G(3,2)`.
The coordinates of point D is ____________

A

(7,-4)

B

(5,0)

C

(7,4)

D

(-3,0)

Text Solution

Verified by Experts

The correct Answer is:
B
Let the coordinates of D be `(alpha,beta)`. Then,
`(alpha+1+3)/(3)=3` or `alpha=5`
and `(beta+2+4)/(3)=2` or `beta=0`
`therefore D-=(5,0)`
Taking `A(x_1,y_1),B(x_1,y_1)`, and `C(x_3,y_3)`, we have
`(x_1+x_2)/(2)=1`,
`(x_2+x_3)/(2) =5, (x_3+x_1)/(2)=3`
and `(y_1+y_2)/(2)=5,(y_2+y_3)/(2)=0,(y_1+y_3)/(2)=4`
Solving the above equations we get
`A-=(-1,6),B-=(3,-2),C-=(7,2)`
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