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
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
Show Hint
Use midpoint property of diagonals in parallelogram.
Updated On: Apr 18, 2026
- \(x+y+6=0\)
- \(x+y-6=0\)
- \(x-y-4=0\)
- \(x-2y-1=0\)
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The Correct Option is B
Solution and Explanation
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: \[ y-1 = -1(x-5) \Rightarrow x+y-6=0 \]
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: \[ y-1 = -1(x-5) \Rightarrow x+y-6=0 \]
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