Use a graph paper to answer the following questions.
(Take 1 cm = 1 unit on both axes) :
(iv) Give a geometrical name for the figure AA'C'B'BC.Here A (4, 4), B (4, -6) and C (8, 0),A' (-4, 4), B'(-4, -6) and C'(-8, 0) the vertices of a triangle ABC.

Answer

To solve the given problem, we will follow these steps:

### Step 1: Plot the Points
We have the points A(4, 4), B(4, -6), C(8, 0), A'(-4, 4), B'(-4, -6), and C'(-8, 0). Using graph paper, we will plot these points.

1. **Point A**: (4, 4) - Move 4 units right on the x-axis and 4 units up on the y-axis.
2. **Point B**: (4, -6) - Move 4 units right on the x-axis and 6 units down on the y-axis.
3. **Point C**: (8, 0) - Move 8 units right on the x-axis and stay on the x-axis (0 on the y-axis).
4. **Point A'**: (-4, 4) - Move 4 units left on the x-axis and 4 units up on the y-axis.
5. **Point B'**: (-4, -6) - Move 4 units left on the x-axis and 6 units down on the y-axis.
6. **Point C'**: (-8, 0) - Move 8 units left on the x-axis and stay on the x-axis (0 on the y-axis).

### Step 2: Connect the Points
Next, we will connect the points in the order specified in the question: A, A', C', B', B, C.

1. Draw a line from A to A'.
2. Draw a line from A' to C'.
3. Draw a line from C' to B'.
4. Draw a line from B' to B.
5. Draw a line from B to C.
6. Draw a line from C to A.

### Step 3: Count the Sides
Now, we will count the number of sides in the figure formed by the connected points.

1. The sides are: A to A', A' to C', C' to B', B' to B, B to C, and C to A.
2. This gives us a total of 6 sides.

### Step 4: Identify the Geometric Figure
Since the figure has 6 sides, we can identify it as a hexagon.

### Final Answer
The geometric name for the figure AA'C'B'BC is a **hexagon**.

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