Question

If \(A(-1,2)\), \(B(5,1)\), \(C(6,5)\) are the vertices of a parallelogram \(ABCD\). The equation to the diagonal through \(B\) is

• A. \(x+y+6=0\)
• B. \(x+y-6=0\)
• C. \(x-y-4=0\)
• D. \(x-2y-1=0\)

Hint:

Use midpoint property of diagonals in parallelogram.

Answer 1

The Correct Option is B

Concept: Diagonals bisect each other.

Step 1: Find midpoint of AC.
\[ M = \left(\frac{-1+6}{2}, \frac{2+5}{2}\right) = \left(\frac{5}{2}, \frac{7}{2}\right) \]

Step 2: Line through B and M.
Slope: \[ m = \frac{7/2 -1}{5/2 -5} = \frac{5/2}{-5/2} = -1 \] Equation: \[ y-1 = -1(x-5) \Rightarrow x+y-6=0 \]