Short answer type questions:

(i) Let us write the value of y if the distance of the point (–4, y) from the origin is 5 units.

(ii) Let us write the co - ordinates of a point on y - axis which is equidistant from two points (2, 3) and (–1, 2).

(iii) Let us write the coordinates of two points on the x-axis and y-axis for which an isosceles right-angled triangle is formed with the x-axis, y-axis and the straight line joining the two points.

(iv) Let us write the co - ordinates of two points on opposite sides of x - axis which are equidistant from x - axis.

(v) Let us write the co - ordinates of two points on opposite sides of y - axis which are equidistant from y - axis.

(i) Distance between two points =

Here the second point is origin.

5 =

Squaring on both sides,

25 = 16 + y²

Or y = + 3 or - 3.

(ii) A point on y-axis will have x coordinate 0.

So, let the point on y-axis be (0, y) .

If this point is equidistant from given two points,

=

Squaring on both sides,

(y - 3) ² + 4 = (y - 2) ² + 1

Or y² - 3y + 9 + 4 = y² - 2y + 4 + 1

13 - 5 = y

y = 8

So the coordinate on the y-axis is (0, 8)

(iii) Let the point on x-axis be A (x, 0)

Let the point on y-axis be B (0, y)

To satisfy the conditions given in the problem,

The distance of A from origin should be the same as the distance of B from origin.

The distance between two points =

Or x= + y or x = - y

The coordinates should be (0, x) and (x, 0) where x is any real number.

(iv) (x, 0) and (- x, 0)

(v) (0, y) and (0, - y)