To find the area of the triangle, we need to determine its base and height.
1. **Identify the vertices:**
- First vertex: (3, 1)
- Second vertex: (1, 7)
- Third vertex: (9, 1)
2. **Determine the base:**
The base is the horizontal distance between the first and third vertices, both of which lie on row 1 (which means they share the same y-coordinate).
- First vertex: (3, 1)
- Third vertex: (9, 1)
The distance between column 3 and column 9 is \(9 - 3 = 6\).
3. **Determine the height:**
The height is the vertical distance between the first or third vertex and the second vertex, since the first and third vertices lie on the same row.
- Second vertex: (1, 7)
The second vertex is on row 7 and the first or third vertex is on row 1.
The distance between row 7 and row 1 is \(7 - 1 = 6\).
4. **Calculate the area of the triangle:**
The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \):
\[
\text{Area} = \frac{1}{2} \times 6 \times 6 = \frac{1}{2} \times 36 = 18 \text{ square units}
\]
Therefore, the area of the non-right triangle is:
**18 square units.**
Use the image to answer the question.
An illustration shows a 10 by 10 grid. A non-right triangle is enclosed within the grid. The first vertex is at the top of row 1 and the right of column 3. The second vertex is at the top of row 7 and the left of column 1. The third vertex is at the top of row 1 and the right of column 9.
What is the area of the non-right triangle? The base and height are found by counting the squares.
(1 point)
Responses
45 square units
45 square units
18 square units
18 square units
27 square units
27 square units
54 square units
1 answer