If `A = (2, (3sqrt3/2))` then coordinates of C taken mirror image along x=0 is

Options

A. `(-2, (3sqrt3)/2)`
B. `(-2- sqrt 6, (3sqrt3+1)/(2sqrt2))`
C. `(-2 sqrt 3, 3/2)`
D. `(0,3)`

Answer

To find the coordinates of point C, which is the mirror image of point A across the line x = 0, we will follow these steps:

### Step 1: Identify the coordinates of point A
Point A is given as \( A = (2, \frac{3\sqrt{3}}{2}) \).

### Step 2: Understand the concept of mirror image across the line x = 0
The line x = 0 is the y-axis. When we take the mirror image of a point across the y-axis, the y-coordinate remains the same, while the x-coordinate changes sign.

### Step 3: Apply the mirror image concept to point A
For point A:
- The x-coordinate is 2. The mirror image across the y-axis will have the x-coordinate as \(-2\).
- The y-coordinate remains unchanged, which is \(\frac{3\sqrt{3}}{2}\).

### Step 4: Write the coordinates of point C
Thus, the coordinates of point C, the mirror image of point A across the line x = 0, will be:
\[ C = (-2, \frac{3\sqrt{3}}{2}) \]

### Final Answer:
The coordinates of point C are \((-2, \frac{3\sqrt{3}}{2})\).

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