Question

Fiona draws a triangle on a coordinate grid with vertices at C (6,2), B (4,6), and A (1,2). What is the area in square units of Fiona's triangle?

The area of the triangle is _ square units.

Answer 1

To find the area of the triangle with vertices at points \( C(6,2) \), \( B(4,6) \), and \( A(1,2) \), we can use the formula for the area of a triangle given by the coordinates of its vertices:

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

Let the coordinates of the vertices be:

- \( A(1, 2) \) has \( x_1 = 1 \), \( y_1 = 2 \)
- \( B(4, 6) \) has \( x_2 = 4 \), \( y_2 = 6 \)
- \( C(6, 2) \) has \( x_3 = 6 \), \( y_3 = 2 \)

Now, substituting these coordinates into the formula:

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

Calculating each term:

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

Now putting it all together:

\[
\text{Area} = \frac{1}{2} \left| 4 + 0 - 24 \right| = \frac{1}{2} \left| 4 - 24 \right| = \frac{1}{2} \left| -20 \right| = \frac{1}{2} \cdot 20 = 10
\]

Thus, the area of Fiona's triangle is

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