Use graph paper for this question (Take 2 cm = 1 unit along both X and Y axis). ABCD is a quadrilateral whose vertices are A (2, 2), B (2, -2), C (0, -1) and D (0, 1). Name two points which are invariant under the above reflection by y-axis.

Answer

To solve the problem, we need to identify the points that remain unchanged when reflected across the y-axis. Let's go through the steps systematically:

### Step 1: Identify the given points of the quadrilateral ABCD.
The vertices of the quadrilateral are:
- A (2, 2)
- B (2, -2)
- C (0, -1)
- D (0, 1)

### Step 2: Understand the reflection across the y-axis.
When a point (x, y) is reflected across the y-axis, its new coordinates become (-x, y). This means that only the x-coordinate changes its sign while the y-coordinate remains the same.

### Step 3: Reflect each point across the y-axis.
- For point A (2, 2):
- Reflected point A' = (-2, 2)

- For point B (2, -2):
- Reflected point B' = (-2, -2)

- For point C (0, -1):
- Reflected point C' = (0, -1) (remains unchanged)

- For point D (0, 1):
- Reflected point D' = (0, 1) (remains unchanged)

### Step 4: Identify the invariant points.
From the reflection results, we see that points C and D have not changed their coordinates after reflection. Therefore, they are invariant under reflection across the y-axis.

### Final Answer:
The two points which are invariant under reflection by the y-axis are:
- C (0, -1)
- D (0, 1)

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