A plane mirror is on y-z plane facing positive x-axis. A point object is present at (10,5). The mirror is translated by 2 units along positive x and 3 units along positive y-direction. Final image of the point object is at

Options

A. (-10,-5)
B. (-8,-3)
C. (-6,5)
D. (-6,-2)

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the initial setup
The plane mirror is located on the y-z plane and is facing the positive x-axis. The point object is at the coordinates (10, 5).

### Step 2: Determine the initial position of the mirror
Since the mirror is on the y-z plane, its position can be considered as x = 0. The mirror reflects light coming from the positive x-direction.

### Step 3: Translate the mirror
The mirror is translated by 2 units along the positive x-direction and 3 units along the positive y-direction.
- The new position of the mirror will be:
- x = 0 + 2 = 2
- y = 0 + 3 = 3
- Therefore, the new position of the mirror is at (2, 3).

### Step 4: Determine the image of the point object
The image of the point object will be located at a position that is symmetrical with respect to the mirror. The image's x-coordinate will be determined by the distance from the object to the mirror.

1. The object is at (10, 5).
2. The mirror is at (2, 3).
3. The distance from the object to the mirror in the x-direction is:
- Distance = 10 - 2 = 8 units.
4. Since the image will be on the opposite side of the mirror, the x-coordinate of the image will be:
- Image x-coordinate = 2 - 8 = -6.

### Step 5: Determine the y-coordinate of the image
The y-coordinate of the image will be the same as the y-coordinate of the object since the mirror is horizontal (y-z plane):
- Object y-coordinate = 5.
- Therefore, the image y-coordinate = 5.

### Step 6: Final coordinates of the image
Combining the x and y coordinates, the final image of the point object is at:
- Image coordinates = (-6, 5).

### Final Answer
The final image of the point object is at (-6, 5).

---