Name the figure formed when we plot the points (0, 0), (4,4) and (0,4) on a graph paper.

Answer

To determine the figure formed by plotting the points (0, 0), (4, 4), and (0, 4) on a graph paper, we can follow these steps:

### Step-by-Step Solution:

1. **Plot the Points**:
- Start by plotting the first point (0, 0). This point is the origin of the graph.
- Next, plot the second point (4, 4). From the origin, move 4 units to the right (along the x-axis) and then 4 units up (along the y-axis).
- Finally, plot the third point (0, 4). From the origin, do not move along the x-axis (stay at 0) and move 4 units up along the y-axis.

2. **Identify the Coordinates**:
- The coordinates of the points plotted are:
- Point A: (0, 0)
- Point B: (4, 4)
- Point C: (0, 4)

3. **Connect the Points**:
- Draw lines to connect the points A, B, and C.
- Connect A (0, 0) to B (4, 4).
- Connect B (4, 4) to C (0, 4).
- Connect C (0, 4) back to A (0, 0).

4. **Analyze the Figure**:
- Observe the shape formed by the three points.
- The line segment from A to C is vertical, while the line segment from A to B is diagonal, and the line segment from B to C is horizontal.
- This forms a triangle.

5. **Determine the Type of Triangle**:
- Check the lengths of the sides:
- The length of AC is 4 units (vertical).
- The length of AB can be calculated using the distance formula:
\[ AB = \sqrt{(4-0)^2 + (4-0)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \]
- The length of BC is also 4 units (horizontal).
- Since two sides (AC and BC) are equal and the angle at A is a right angle (90 degrees), this triangle is an isosceles right triangle.

### Conclusion:
The figure formed by the points (0, 0), (4, 4), and (0, 4) is an **isosceles right triangle**.