Find the point on X axis which is equidistant from the points M (-5,-2) and N (-3,-2).

To find the point on the X axis that is equidistant from points M(-5,-2) and N(-3,-2), we first need to understand that any point on the X axis has a Y-coordinate of 0.

The formula for the distance between two points (x1, y1) and (x2, y2) is sqrt((x2-x1)^2 + (y2-y1)^2).

Given that the point we're looking for is equidistant from M and N, we can set up the following equation:

sqrt((x-(-5))^2 + (0-(-2))^2) = sqrt((x-(-3))^2 + (0-(-2))^2)

Solving this equation will give us the X-coordinate of the point we're looking for.

Squaring both sides to get rid of the square root gives us:

(x+5)^2 + 4 = (x+3)^2 + 4

Solving this equation gives us x = -4.

So, the point on the X axis that is equidistant from M(-5,-2) and N(-3,-2) is (-4, 0).