Question

write the coordinates of a point on each of the axes such that they are equidistant from the origin ​

Answer 1

The co-ordinate of a point, won on the x axis and the other on the y-axis, so that the two points are equidistant from the origin are as follows;;

let's assume that the point is at a distance a from the x-axis and the y-axes respectively, then, by simple co-ordinate geometry, the co-ordinate x and y will be a and a respectively, so we can write it as (a,a).

Now, such a point has a property, here we can see the x and y co-ordinate are same, so the right Triangle formed will have the 2 legs equal, so a line drawn from origin passing through (a,a) will have an angle of 45° with both the axis. So the Slope of such a line will be tan45° or 1. And all the points on such a line will have coordinates of the from (a,a).

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