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The coordinates of the point which is equidistant from the three vertices of △AOB (shown in the adjoining figure) are

The coordinates of the point which is equidistant from the three vertices of △AOB(shown in the given figure) are (a) (x, y) (b) (y, x) (c) (x/2, y/2) (d) (y/2, x/2). Section Formula, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

  1. (x, y)

  2. (y, x)

  3. (x2,y2)\Big(\dfrac{x}{2}, \dfrac{y}{2}\Big)

  4. (y2,x2)\Big(\dfrac{y}{2}, \dfrac{x}{2}\Big)

Section Formula

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Answer

Since the triangle AOB is the right angled triangle the point which is equidistant from O, A and B is the mid-point of AB. Let that mid-point be D.

Applying mid-point formula, coordinates are,

=0+2x2,2y+02=2x2,2y2=(x,y).= \dfrac{0 + 2x}{2}, \dfrac{2y + 0}{2} \\[1em] = \dfrac{2x}{2}, \dfrac{2y}{2} \\[1em] = (x, y).

Hence, Option 1 is the correct option.

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