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P (4, (2) and R (–2, 0) are vertices of a rhombus PQRS. What is the equation of diagonal QS ?
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- x – 3y = – 2
- 3x + y = 4
- 3 x + y = –4
- x – 3y = 2
- x – 3y = – 2
Correct Option: B
The diagonals of a rhombus bisect each other at right angles.
∴ Co-ordinates of point ‘O’
| = |  | , |  | ||
| 2 | 2 |
| = | | , | | = (1 , 1) | |||
| 2 | 2 |
Slope of straight line PR
| = | = | ||
| x2 - x1 | -2 - 4 |
| = | = | ||
| - 6 | 3 |
∵ PR ⊥ QS
| ∴ Slope of QS = – | = - 3 | ||
| 3 | |||
[∵ m1 m2 = – 1]
∴ Equation of straight line QS passing through point (1, 1) : y – 1 = – 3 (x – 1)
⇒ y – 1 = –3 x + 3
⇒ 3x + y = 4
