Question

How many points are there on the x-axis, at a distance 5 from the point (1, 3)? What are their coordinates? What about such points on the y-axis?

Answer 1

Let the given point be A (1, 3).

On x-axis:

Let the coordinates of the required points be (h, k). But since the points lie on the x-axis, the y-coordinate should be zero.

So, the coordinates of the required points are (h, 0).

We know that distance between two points is given by:

D =

The required point is at a distance of 5 units from the point A

Thus, there are two points on the x -axis which are at a distance of 5 units from the point (1, 3) and their coordinates are (−3, 0) and (5, 0).

On y-axis:

Let the coordinates of the required points be (h, k). But since the points lie on the y-axis, the x-coordinate should be zero.

So, the coordinates of the required points are (0, k).

The required point is at a distance of 5 units from the point A

Thus, there are two points on y-axis which are at a distance of 5 units from the point (1, 3) and their coordinates are