Plot the point `A(2, 5), B(-2, 2) and C(4,2)` on a graph paper. Join AB, BC and AC. Calculate the area of `triangleABC`.

Answer

To solve the problem of plotting the points \( A(2, 5) \), \( B(-2, 2) \), and \( C(4, 2) \) on a graph paper and calculating the area of triangle \( ABC \), we can follow these steps:

### Step 1: Plot the Points
1. **Plot Point A(2, 5)**:
- Move 2 units along the x-axis (to the right) and 5 units up along the y-axis. Mark this point as A.

2. **Plot Point B(-2, 2)**:
- Move 2 units along the x-axis (to the left) and 2 units up along the y-axis. Mark this point as B.

3. **Plot Point C(4, 2)**:
- Move 4 units along the x-axis (to the right) and 2 units up along the y-axis. Mark this point as C.

### Step 2: Join the Points
- Draw line segments to connect points A, B, and C:
- Join A to B (line segment AB).
- Join B to C (line segment BC).
- Join C to A (line segment AC).

### Step 3: Calculate the Area of Triangle ABC
To find the area of triangle \( ABC \), we can use the formula:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

#### Step 3.1: Identify the Base and Height
- **Base**: We can take BC as the base.
- The coordinates of B are \((-2, 2)\) and C are \((4, 2)\).
- The length of base BC is calculated as:

\[ \text{Base} = |x_C - x_B| = |4 - (-2)| = |4 + 2| = 6 \text{ units} \]

- **Height**: The height is the perpendicular distance from point A to line BC.
- The y-coordinate of point A is 5, and the y-coordinate of points B and C is 2. Thus, the height is:

\[ \text{Height} = |y_A - y_{BC}| = |5 - 2| = 3 \text{ units} \]

#### Step 3.2: Calculate the Area
Now we can substitute the base and height into the area formula:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 3 = \frac{18}{2} = 9 \text{ square units} \]

### Final Answer
The area of triangle \( ABC \) is \( 9 \) square units.

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