The distance of the midpoint of the line segm | vedclass

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(A) Let the points be $P(a \sin 	heta, 0)$ and $Q(0, a \cos 	heta)$.The midpoint $M$ of the line segment $PQ$ is given by the formula $\left( \frac{

Vedclass · Accepted Answer

$\frac{a}{2}$

Vedclass · Answer

(A) Let the points be $P(a \sin 	heta, 0)$ and $Q(0, a \cos 	heta)$.The midpoint $M$ of the line segment $PQ$ is given by the formula $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} ight)$.Substituting the coordinates,$M = \left( \frac{a \sin 	heta + 0}{2}, \frac{0 + a \cos 	heta}{2} ight) = \left( \frac{a \sin 	heta}{2}, \frac{a \cos 	heta}{2} ight)$.The distance of $M$ from the origin $(0, 0)$ is $\sqrt{\left( \frac{a \sin 	heta}{2} - 0 ight)^2 + \left( \frac{a \cos 	heta}{2} - 0 ight)^2}$.$= \sqrt{\frac{a^2 \sin^2 	heta}{4} + \frac{a^2 \cos^2 	heta}{4}} = \sqrt{\frac{a^2}{4} (\sin^2 	heta + \cos^2 	heta)}$.Since $\sin^2 	heta + \cos^2 	heta = 1$,the distance is $\sqrt{\frac{a^2}{4}} = \frac{a}{2}$.

The distance of the midpoint of the line segment joining the points $(a \sin \theta, 0)$ and $(0, a \cos \theta)$ from the origin is:

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