The equation of the diagonal through origin of the quadrilateral formed by the lines $X = 0, Y = 0, X + Y - 1 = 0$ and $6 x + Y - 3 = 0$ is :

4 x - 3 y = 0

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3 x - 2 y = 0

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x = y

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x + y = 0

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Solution

The correct option is C $3 x - 2 y = 0$
$G i v e n - A q u a d r i l a t e r a l w i t h d i a g o n a l A B h a s t h e e q u a t i o n s o f t h e s i d e s a s x = 0, y = 0, x + y - 1 = 0 & 6 x + y - 3 = 0. T h e c o o r d i n a t e s o f A i s t h e o r i g i n . T o f i n d o u t - t h e e q a t i o n o f A B . S o l u t i o n - x = 0 a n d y = 0 i n t e r s e c t a t A (0, 0) . S o B i s t h e p o i n t o f i n t e r s e c t i o n o f t h e l i n e s x + y - 1 = 0...... (i) & 6 x + y - 3 = 0.......... (i i) . F r o m (i) 6 x + 6 y - 6 = 0....... (i i i) . S u b t r a c t i n g (i i) f r o m (i i i), y = \frac{3}{5} . P u t t i n g y = \frac{3}{5} i n (i), x + \frac{3}{5} - 1 = 0 ⟹ x = \frac{2}{5} . ∴ B (\frac{2}{5}, \frac{3}{5}) i s t h e p o i n t o f t h e v e r t e x o p p o s i t e t o A . E q u a t i o n o f t h e d i a g o n a l A B i s \frac{y - 0}{\frac{3}{5} - 0} = \frac{x - 0}{\frac{2}{5} - 0} ⟹ 3 x - 2 y = 0.$

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Similar questions

Q. The diagonal passing through origin of a quadrilateral formed by

x = 0, y = 0, x + y = 1

and

6 x + y = 3

Q. Find the equation of the circle which circumscribes the triangle formed by the lines
(i) x + y + 3 = 0, x − y + 1 = 0 and x = 3
(ii) 2x + y − 3 = 0, x + y − 1 = 0 and 3x + 2y − 5 = 0
(iii) x + y = 2, 3x − 4y = 6 and x − y = 0.
(iv) y = x + 2, 3y = 4x and 2y = 3x.

Find the equation of the circle which circumscribes the triangle formed by the lines:
(i) $x + y + 3 = 0, x - y + 1 = 0$ and $x = 3$
(ii) $2 x + y - 3 = 0, x + y - 1 = 0$ and $3 x + 2 y - 5 = 0$
(iii) $x + y = 2, 3 x - 4 y = 6$ and $x - y = 0.$
(iv) $y = x + 2, 3 y = 4 x$ and $2 y = 3 x$ .

Q. The area of triangle formed by the lines x + y - 3 = 0, x - 3y + 9 = 0 and 3x - 2y + 1 = 0 is

Q. The line

3 x + 2 y = 6

will divide the quadrilateral formed by the lines

x + y = 5, y - 2 x = 8, 3 y + 2 x = 0

4 y - x = 0

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The equation of the diagonal through origin of the quadrilateral formed by the lines X=0,Y=0,X+Y−1=0 and 6x+Y−3=0 is :

The equation of the diagonal through origin of the quadrilateral formed by the lines $X = 0, Y = 0, X + Y - 1 = 0$ and $6 x + Y - 3 = 0$ is :