Draw a triangle ABC on graph paper having the coordinates of its vertices as A (-2, 0), B (4, 0) and C (1,5). Also find the area of triangle.

Answer

### Step-by-Step Solution:

1. **Plot the Points:**
- Start by plotting the given points A, B, and C on graph paper.
- A has coordinates (-2, 0). Move 2 units to the left on the x-axis and stay at 0 on the y-axis. Mark this point as A.
- B has coordinates (4, 0). Move 4 units to the right on the x-axis and stay at 0 on the y-axis. Mark this point as B.
- C has coordinates (1, 5). Move 1 unit to the right on the x-axis and 5 units up on the y-axis. Mark this point as C.

2. **Draw the Triangle:**
- Connect the points A, B, and C with straight lines to form triangle ABC.

3. **Identify the Base and Height:**
- The base of the triangle can be considered as the line segment AB. To find its length, count the distance between points A and B along the x-axis:
- Length of base AB = |x_B - x_A| = |4 - (-2)| = |4 + 2| = 6 units.
- The height of the triangle can be measured as the perpendicular distance from point C to the line AB (which lies on the x-axis). Since point C is at (1, 5), the height is simply the y-coordinate of point C:
- Height = 5 units.

4. **Calculate the Area:**
- Use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]
- Substitute the values of base and height:
\[ \text{Area} = \frac{1}{2} \times 6 \times 5 = \frac{30}{2} = 15 \text{ square units} \]

### Final Answer:
The area of triangle ABC is **15 square units**.

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