Introduction:
To find a point on the x-axis at a distance of 4 units from point A(2,1), we can use the distance formula and the properties of the x-axis.

Distance Formula:
The distance formula is used to calculate the distance between two points in a coordinate plane. It can be used to find the distance between point A(2,1) and any other point on the x-axis.

The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where:
- d represents the distance between two points
- (x1, y1) and (x2, y2) are the coordinates of the two points

In this case, we want to find a point on the x-axis, which means the y-coordinate will be 0.

Steps to Find the Point:
1. Set y2 = 0, as the point we are looking for lies on the x-axis.
2. Substitute the given values into the distance formula.
3. Simplify the equation and solve for x2.
4. Once we have the x-coordinate, we can find the point by substituting it into the equation for the x-axis, y = 0.

Calculation:
Let's calculate the point on the x-axis at a distance of 4 units from point A(2,1) using the steps mentioned above.

1. Set y2 = 0.
- (x1, y1) = (2, 1)
- (x2, y2) = (x, 0)

2. Substitute the values into the distance formula.
d = sqrt((x - 2)^2 + (0 - 1)^2)

3. Simplify the equation and solve for x.
4 = sqrt((x - 2)^2 + 1)
16 = (x - 2)^2 + 1
15 = (x - 2)^2
±√15 = x - 2
x = 2 ± √15

4. Find the point on the x-axis.
Point 1: (2 + √15, 0)
Point 2: (2 - √15, 0)

Conclusion:
The points on the x-axis at a distance of 4 units from point A(2,1) are (2 + √15, 0) and (2 - √15, 0). These points satisfy the given conditions and can be found using the distance formula and the properties of the x-axis.

Please help me