Point `P(2,3)` goes through following transformations in successtion:
(i) reflection in line `y=x`
(ii) translation of 4 units to the right
(iii) translation of 5 units up
(iv) reflection in y-axis
Find the coordinates of final position of the point .

Explanation

To find the final coordinates of point \( P(2,3) \) after a series of transformations, we will go through each transformation step by step.

### Step 1: Reflection in the line \( y = x \)

When a point \( (x, y) \) is reflected in the line \( y = x \), the coordinates swap places. Therefore, the reflection of point \( P(2, 3) \) will be:

\[ P_1 = (3, 2) \]

### Step 2: Translation of 4 units to the right

Translating a point to the right means adding to the x-coordinate. So, we add 4 to the x-coordinate of \( P_1(3, 2) \):

\[ P_2 = (3 + 4, 2) = (7, 2) \]

### Step 3: Translation of 5 units up

Translating a point upwards means adding to the y-coordinate. We add 5 to the y-coordinate of \( P_2(7, 2) \):

\[ P_3 = (7, 2 + 5) = (7, 7) \]

### Step 4: Reflection in the y-axis

When a point \( (x, y) \) is reflected in the y-axis, the x-coordinate changes sign. Therefore, the reflection of point \( P_3(7, 7) \) will be:

\[ P_4 = (-7, 7) \]

### Final Coordinates

After performing all the transformations, the final coordinates of the point are:

\[ \text{Final Position} = P_4 = (-7, 7) \]

### Summary of Steps

1. **Reflection in line \( y = x \)**: \( P(2, 3) \) → \( P_1(3, 2) \)
2. **Translation of 4 units to the right**: \( P_1(3, 2) \) → \( P_2(7, 2) \)
3. **Translation of 5 units up**: \( P_2(7, 2) \) → \( P_3(7, 7) \)
4. **Reflection in y-axis**: \( P_3(7, 7) \) → \( P_4(-7, 7) \)