Question

The distance of the middle point of the line joining two points $(a\sin \theta ,0),(0,a\cos \theta )$ from the origin is-

• A. $a$
• B. $a/2$
• C. $a(\sin \theta +\cos \theta )/2$
• D. $a(\sin \theta +\cos \theta )$

Answer 1

The correct option is B $a/2$

Given the two points are-$(aSin\theta ,0),(0,aCos\theta )$

Distance between two points are $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

=$(\frac{aSin\theta +0}{2},\frac{0+aCos\theta }{2})$

=$(\frac{aSin\theta }{2},\frac{aCos\theta }{2})$

Now the distance of the middle point of the line joining two points are-

$D=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$=\sqrt{(0-\frac{aSin\theta }{2}{)}^2+(0-\frac{aCos\theta }{2}{)}^2}$

$=\sqrt{(\frac{aSin\theta }{2}{)}^2+(\frac{aCos\theta }{2}{)}^2}$

$=\frac{a}{2}\sqrt{Si{n}^2\theta +Co{s}^2\theta }$

$=\frac{a}{2}$

The correct option is B