The point Q (a, b) is first reflected in y - axis to Q1 which is then reflected in x - axis to ( - 5, 3) . The co - ordinates of point Q are

Options

A. (-5, - 3)
B. (5, 3)
C. (-5, 3)
D. (5, -3)

Answer

To find the coordinates of point Q (a, b), we will follow the steps of reflection as described in the problem.

### Step-by-Step Solution:

1. **Reflection in the y-axis**:
- When a point (a, b) is reflected in the y-axis, the x-coordinate changes its sign. Therefore, the coordinates of the reflected point Q1 will be (-a, b).

2. **Reflection in the x-axis**:
- Next, the point Q1 (-a, b) is reflected in the x-axis. When reflecting a point across the x-axis, the y-coordinate changes its sign. Thus, the coordinates of the reflected point Q2 will be (-a, -b).

3. **Given coordinates of Q2**:
- We know that the final reflected point Q2 is (-5, 3). Therefore, we can set up the following equations based on the reflections:
- From the x-coordinate: -a = -5
- From the y-coordinate: -b = 3

4. **Solving for a and b**:
- From the equation -a = -5, we can multiply both sides by -1 to find:
\[ a = 5 \]
- From the equation -b = 3, we can multiply both sides by -1 to find:
\[ b = -3 \]

5. **Coordinates of point Q**:
- Now that we have the values of a and b, the coordinates of point Q (a, b) are:
\[ Q(5, -3) \]

### Final Answer:
The coordinates of point Q are (5, -3).

---