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JEE Main 201911 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
11 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2019 · 11 January · Evening Shift · Mathematics · Straight Lines

If in a parallelogram ABDC , the coordinates of A, B and C are...

If in a parallelogram ABDC\mathrm{ABDC}, the coordinates of A,B\mathrm{A}, \mathrm{B} and C\mathrm{C} are respectively (1,2),(3,4)and(2,5),and (2,5), then the equation of the diagonal AD\mathrm{AD} is :If in a parallelogram ABDC , the coordinates of A, B and C are respectively (1,2),(3,4) and (2,5), then the equation of

Options

  1. A5x−3y+1=05 x-3 y+1=0
  2. B5x+3y−11=05 x+3 y-11=0
  3. C3x−5y+7=03 x-5 y+7=0
  4. D3x+5y−13=03 x+5 y-13=0

Correct answer

A. 5x−3y+1=05 x-3 y+1=0

Step-by-step solution

Since, in parallelogram mid points of both diagonals coinsides. ∴\therefore mid-point of AD=A D= mid-point of BCB C If in a parallelogram ABDC , the coordinates of A, B and C are respectively (1,2),(3,4) and (2,5), then the equation of
(x1+12,y1+22)=\left(\frac{x_{1}+1}{2}, \frac{y_{1}+2}{2}\right)=\left(\frac{3+2}{2}, \frac{4+5}{2}\right) \therefore \quad\left(x_{1}, y_{1}\right)=(4,7)Then,equationofThen, equation ofA Dis,is,y-7=\frac{2-7}{1-4}(x-4) y-7=\frac{5}{3}(x-4) 3 y-21=5 x-20 5 x-3 y+1=0
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