To draw a triangle that has an area of 27 square units, we can use the concept of the area of a triangle given its vertices. Here is how you can determine the points step-by-step:
1. Determine the points of the triangle:
We need to select three points in a 2-dimensional coordinate system. Let's choose the points (0, 0), (9, 0), and (0, 6).
2. Vertices of the triangle:
- Point A: (0, 0)
- Point B: (9, 0)
- Point C: (0, 6)
3. Draw the triangle:
- Start by plotting point A at the origin (0, 0).
- Next, plot point B at (9, 0) on the x-axis.
- Finally, plot point C at (0, 6) on the y-axis.
4. Connect the points:
- Draw a line segment from point A (0, 0) to point B (9, 0).
- Draw a line segment from point B (9, 0) to point C (0, 6).
- Draw a line segment from point C (0, 6) back to point A (0, 0).
5. Verify the area:
- The vertices (0, 0), (9, 0), and (0, 6) form a right triangle.
- The base of the triangle (horizontal line segment AB) is 9 units.
- The height of the triangle (vertical line segment AC) is 6 units.
- Using the formula for the area of a triangle:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\][/tex]
- Substitute the values:
[tex]\[
\text{Area} = \frac{1}{2} \times 9 \times 6 = 27 \text{ square units}
\][/tex]
So, the triangle with vertices at (0, 0), (9, 0), and (0, 6) will have an area of 27 square units.
