Question

The straight lines $4x-3y-5=0,x-2y-10=0,7x+y-40=0$ and $x+3y+10=0$ form the sides of a

• A. plain quadrilateral
• B. cyclic quadrilateral
• C. rectangle
• D. parallelogram

Answer 1

Answer: (B)

cyclic quadrilateral

Slopes of the lines are $\frac{4}{3},\frac{1}{2}-7$ and $-\frac{1}{3}$ respectively.

If $A$ is the angle between first and third, $B$ is the angle between second and fourth.

Then $\tan A=-1,\tan B=1\Rightarrow A={135}^0,B={45}^0\Rightarrow A+B={180}^0$

So the quadrilateral is cyclic.

Since no two sides are parallel , it can not be parallelogram or rectangle.