Question

In the given diagram, ΔAOB is a right-angled triangle and C is the mid-point of AB. The coordinates of the point which is equidistant from the three vertices of ΔAOB is:

Options

• (x, y)

• (y, x)

• `(x/2, y/2)`

• `((2x)/3, (2y)/3)`

Answer 1

(x, y)

Explanation:

Given: C is the midpoint of AB.

We know that,

In a right-angled triangle, the point equidistant from all three vertices is the midpoint of the hypotenuse.

Using the midpoint formula:

`M = ((x_1 + x_2)/2, (y_1 + y_2)/2)`

Substituting values, we get:

⇒ C = `((0 + 2x)/2, (2y + 0)/2)`

⇒ C = `((2x)/2, (2y)/2)`

⇒ C = (x, y)