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Area

The diagonals...

Question

The diagonals of a parallelogram $A B C D$ are along the lines $x + 3 y = 4$ and $6 x - 2 y = 7 .$ Then $A B C D$ must be a

A

rectangle

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B

square

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C

cyclic quadrilateral

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D

rhombus

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Solution

The correct option is D rhombus
$\begin{matrix} S l o p e o f l i n e x + 3 y = 4 m_{1} = \frac{1}{3} s l o p e o f l i n e 6 x - 2 y = 7 m_{2} = \frac{6}{- 2} = - 3 m_{1} \times m_{2} = - 1 H e n c e, b o t h d i a g o n a l a r e p e r p e n d i c u l a r t o e a c h o t h e r . F u r t h e r, i n R h o m b u s a r e p e r p e n d i c u l a r t o e a c h o t h e r . \end{matrix}$
Hence,
option $D$ is correct answer.

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Similar questions

Q. The diagnols of a parallelogram

P Q R S

are along the line

x + 3 y = 4

6 x - 2 y = 7

P Q R S

A B C D

be parallelogram whose equations for the diagonals

A C

B D

x + 2 y = 3

2 x + y = 3

, respectively. If length of diagonal

A C = 4

units and area of parallologram

A B C D = 8

sq. units then the length of other diagonal

B D

A B C D

is inscribed in a circle with a diameter lying along the line

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\to A C, \to B D

are its diagonals Then,

\to A C - \to B D

Q. If the diagonals of a parallelogram ABCD are equal then ∠ABC = ___________.

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