question_answer

If A and B are the points \[(-3,4)\] and \[(2,1)\] respectively, then the coordinates of the point on AB produced such that \[\text{AC}=\text{2BC}\] we:

A) \[(2,4)\]

B) \[(3,7)\]

C) \[(7,-2)\]

D) None of these

Correct Answer: C

Solution :

[c]

If \[AC=2BC\,\,\Rightarrow \,\,B\] is mid-point of AC.

\[\frac{-3+x}{2}=2,\]and \[\frac{4+y}{2}=1\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=7,\] and \[y=-2\]

\[\therefore \]  Coordinates of Care \[(7,-2).\]