Use graph paper to answer the following questions.
(Take 2 cm = 1 unit on both axis).
(iv) Write the geometric name of the figure ABA'B'.the points A (-4, 2) and B (2, 4) ,A‘(4,2),B’(2,0).

Answer

To solve the problem, we need to plot the points A, B, A', and B' on a graph paper and then analyze the figure formed by these points.

### Step-by-Step Solution:

1. **Identify the Points**:
- A(-4, 2)
- B(2, 4)
- A'(4, 2)
- B'(2, 0)

2. **Set Up the Graph**:
- Use graph paper and mark the axes. Since 2 cm = 1 unit, each unit on the graph will be represented by 2 cm.

3. **Plot the Points**:
- **Point A**: From the origin (0,0), move 4 units to the left (negative x-direction) and 2 units up (positive y-direction). Mark this point as A.
- **Point B**: From the origin, move 2 units to the right (positive x-direction) and 4 units up (positive y-direction). Mark this point as B.
- **Point A'**: From the origin, move 4 units to the right (positive x-direction) and 2 units up (positive y-direction). Mark this point as A'.
- **Point B'**: From the origin, move 2 units to the right (positive x-direction) and 0 units up (on the x-axis). Mark this point as B'.

4. **Connect the Points**:
- Draw lines to connect the points in the order A, B, A', B'. This will form a quadrilateral.

5. **Analyze the Figure**:
- Observe the shape formed by the points A, B, A', and B'.
- Notice that the lines AA' and BB' are perpendicular to each other and that the adjacent sides AB and A'B' are equal in length.

6. **Determine the Geometric Name**:
- Since the figure has two pairs of equal adjacent sides and the diagonals intersect at right angles, the geometric name of the figure ABA'B' is a **kite**.

### Final Answer:
The geometric name of the figure ABA'B' is a **kite**.