The image of the point A(1,2) by the line mirror y=x is the point B and the image of B by the line mirror y=0 is the point `(alpha, beta)` then

Options

A. `alpha=1,beta=-2`
B. `alpha=0,beta=0`
C. `alpha=2,beta=-1`
D. None of these

Answer

To solve the problem step by step, we will find the image of point A(1, 2) first by the line y = x, and then find the image of that resulting point by the line y = 0.

### Step 1: Find the image of point A(1, 2) by the line y = x.

The line y = x reflects points across the line. To find the image of a point (x, y) across the line y = x, we simply swap the coordinates.

For point A(1, 2):
- The x-coordinate is 1 and the y-coordinate is 2.
- After swapping, the coordinates of point B will be (2, 1).

**Point B = (2, 1)**

### Step 2: Find the image of point B(2, 1) by the line y = 0.

The line y = 0 is the x-axis. To find the image of a point (x, y) across the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.

For point B(2, 1):
- The x-coordinate is 2 and the y-coordinate is 1.
- The image across the x-axis will be (2, -1).

**Point (alpha, beta) = (2, -1)**

### Final Result:
Thus, we have:
- α = 2
- β = -1