Question

Two line segments AB and CD are taken. Initially the points A & C and B & D are coincident. The line segment CD is rotated about point D such that D and B continue to be coincident but no other points are coincident. CD is rotated such that it becomes coincident to AB again and the distance covered by point C is x. If the distance covered by C is y which is less than x and the angle subtented by CD with respect to starting point is θ, then find the relation among x,y and θ. Assume that θ is in degrees.

• A. x = (y × θ)/360
• B. x = (y × θ)/180
• C. y = (x × θ)/360
• D. y = (x × θ)/260

Answer 1

The correct option is C

y = (x × θ)/360

We can see that if BC moves one full revolution, C covers the circumference of the circle which is given by $x$.

One full revolution is ${360}^{\circ }$ of the angular displacement. For an angular displacement of θ¸ the movement of C is y.

Hence, $x$ is proportional to ${360}^{\circ }$ and y to θ degrees. Thus $\frac{x}{360}$ = $\frac{y}{\theta }$¸

So, y = $\frac{(x\times \theta )}{360}$