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MHT CET · Maths · Straight Lines

The points \((1,3)\) and \((5,1)\) are two opposite vertices of a rectangle. The other two vertices are lie on the line \(\mathrm{y}=2 x+\mathrm{c}\) where c is the constant, then co-ordinates of other two vertices are

  1. A \((4,4),(2,0)\)
  2. B \((4,4),(1,0)\)
  3. C \((2,0),(4,1)\)
  4. D \((2,0),(1,-1)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \((4,4),(2,0)\)

Step-by-step Solution

Detailed explanation

Midpoint of opposite vertices \((1,3)\) and \((5,1)\): \(M = \left(\frac{1+5}{2}, \frac{3+1}{2}\right) = (3,2)\). Midpoint \(M(3,2)\) lies on the line \(y = 2x+c\): \(2 = 2(3)+c \Rightarrow c = -4\).