Question

I take 2 line segments AB and CD. Initially I keep them coincident so that points A & C and points B & D are coincident. Now I start to rotate line segment

CD about point D so that D and B continue to be coincident, but no other points on the 2 line segments are coincident anymore. If CD is rotated till AB and

CD become coincident again, the distance covered by point C is $x$. Instead, if the distance covered byC is a distance y which is less than $x$, and the

angle covered by CD with respect to its starting position is $\theta$, then find the relation between $x$, y and $\theta$. Here assume that angle $\theta$

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