Straight Line and Pair of Straight Lines 1 Question 12
12. If in a parallelogram $A B D C$, the coordinates of $A, B$ and $C$ are respectively $(1,2),(3,4)$ and $(2,5)$, then the equation of the diagonal $A D$ is
(2019 Main, 11 Jan II)
(a) $3 x+5 y-13=0$
(b) $3 x-5 y+7=0$
(c) $5 x-3 y+1=0$
(d) $5 x+3 y-11=0$
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Solution:
- According to given information, we have the following figure
We know that, diagonals of a parallelogram intersect at mid-point.
$\therefore P=$ Mid-point of $B C$ and so, $P \equiv \frac{5}{2}, \frac{9}{2}$
Now, equation of $A D$ is.
$$ \begin{array}{rlrl} & & (y-2)=\frac{\frac{9}{2}-2}{\frac{5}{2}-1}(x-1) \\ \Rightarrow & & y-2 & =\frac{5}{3}(x-1) \\ \Rightarrow & 3 y-6 & =5 x-5 \\ \Rightarrow & & 5 x-3 y & +1=0 \end{array} $$
