Question

Fiona draws a triangle on a coordinate grid with vertices at (6,2) , (4,6) , and (1,2) . What is the area in square units of Fiona’s triangle? (1 point) The area of the triangle is square units.​​​​​​​

Answer 1

To find the area of a triangle given its vertices on a coordinate grid, we can use the formula for the area \( A \) based on the coordinates of the vertices \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \):

\[
A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\]

For the triangle with vertices at \( (6, 2) \), \( (4, 6) \), and \( (1, 2) \), we can assign:
- \( (x_1, y_1) = (6, 2) \)
- \( (x_2, y_2) = (4, 6) \)
- \( (x_3, y_3) = (1, 2) \)

Substituting these coordinates into the area formula:

\[
A = \frac{1}{2} \left| 6(6 - 2) + 4(2 - 2) + 1(2 - 6) \right|
\]

Calculating each term:

1. \( 6(6 - 2) = 6 \times 4 = 24 \)
2. \( 4(2 - 2) = 4 \times 0 = 0 \)
3. \( 1(2 - 6) = 1 \times (-4) = -4 \)

Now we substitute these values into the area formula:

\[
A = \frac{1}{2} \left| 24 + 0 - 4 \right| = \frac{1}{2} \left| 20 \right| = \frac{1}{2} \times 20 = 10
\]

Thus, the area of Fiona’s triangle is

\[
\boxed{10} \text{ square units.}
\]