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

Options

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

Answer

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

### Step 1: Reflection about the line y = x
When a point (a, b) is reflected about the line y = x, the coordinates of the point are swapped. Therefore, the reflection of the point (4, 1) will be:

\[ \text{Reflected point} = (1, 4) \]

### Step 2: Translation through a distance of 2 units along the positive x-axis
To translate a point (x, y) along the positive x-axis, we add the distance to the x-coordinate. Since we need to translate the point (1, 4) by 2 units along the positive x-axis, we will calculate:

\[ \text{New x-coordinate} = 1 + 2 = 3 \]
\[ \text{New y-coordinate} = 4 \]

Thus, the new coordinates after the translation are:

\[ \text{New point} = (3, 4) \]

### Final Answer
The coordinates of the new point after the two transformations are (3, 4).

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