Question

In the given figure, A(0, 2y) and B(2x, 0) are the end-points of line segment AB. The coordinates of point C, which is equidistant from the three vertices of ∆AOB, are


(a) (x , y)
(b) (y , x)
(c) $\left(\frac{x}{2},\frac{y}{2}\right)$
(d) $\left(\frac{y}{2},\frac{x}{2}\right)$

Answer 1

(a) (x , y)
The midpoint of AB is equidistant from the three vertices of $∆AOB.$
Therefore,
$$\begin{gathered} \text{Midpoint of}AB=\left(\frac{0+2x}{2},\frac{2y+0}{2}\right)\left[A\left(0,2y\right)\text{and}B\left(2x,0\right)\Rightarrow \left(x_1=0,y_1=2y\right)\text{and}\left(x_2=2x,y_2=0\right)\right] \\ \text{i.e.}\left(x,y\right) \end{gathered}$$
Hence, the coordinates of C are (x, y).