The point `(4,1)` undergoes the following two successive transformations
(i) Reflection about the line `y=x`
(ii) Translation through a distance 2 units along the positive X-axis.
Then the final coordinate of the point are

Options

A. `(4,3)`
B. `(3,4)`
C. `(1,4)`
D. `((7)/(2),(7)/(2))`

Explanation

To solve the problem step by step, we will perform the two transformations on the point (4, 1) as described.

### Step 1: Reflection about the line y = x

When reflecting a point (x, y) about the line y = x, the coordinates of the point are interchanged.

For the point (4, 1):
- The x-coordinate becomes the y-coordinate.
- The y-coordinate becomes the x-coordinate.

Thus, the reflection of the point (4, 1) about the line y = x is:
\[ (4, 1) \rightarrow (1, 4) \]

### Step 2: Translation through a distance of 2 units along the positive X-axis

Translation along the positive X-axis means we will add the distance to the x-coordinate of the point.

For the reflected point (1, 4):
- We add 2 to the x-coordinate.

Thus, the translation of the point (1, 4) is:
\[ (1, 4) \rightarrow (1 + 2, 4) = (3, 4) \]

### Final Coordinates

After performing both transformations, the final coordinates of the point are:
\[ (3, 4) \]