question_answer

D is a point on AC of the triangle with vertices A \[(2,3)\], \[B(1,-3)\], \[C(-4,-7)\] and BD divides ABC into two triangles of equal area. The equation of the line drawn though B at right angles to BD is

A) \[y-2x+5=0\]

B) \[2y-x+5=0\]

C) \[y+2x-5=0\]

D) \[2y+x-5=0\]

Correct Answer: A

Solution :

[a] Since, the line BD divides the triangle into two of equal area. BD is median and D is (-1, -2). Slope of \[BD=-\frac{1}{2}.\] So, the required line is \[y+3=2(x-1)\] \[\Rightarrow y-2x+5=0\]