SATHEE: Straight Line and Pair of Straight Lines 1 Question 12

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) $3 x - 5 y + 7 = 0$

(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.

$∴ P =$ Mid-point of $B C$ and so, $P \equiv \frac{5}{2}, \frac{9}{2}$

Now, equation of $A D$ is.

$\begin{aligned} (y - 2) = \frac{\frac{9}{2} - 2}{\frac{5}{2} - 1} (x - 1) \\ \Rightarrow & y - 2 & = \frac{5}{3} (x - 1) \\ \Rightarrow & 3 y - 6 & = 5 x - 5 \\ \Rightarrow & 5 x - 3 y & + 1 = 0 \end{aligned}$

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

Solution:

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Straight Line and Pair of Straight Lines 1 Question 12

12. 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 the diagonal AD is

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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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