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?

Answer 1

To find the area of the triangle with vertices at the coordinates \((6, 2)\), \((4, 6)\), and \((1, 2)\), we can use the formula for the area of a triangle given by its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):

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

Assigning the vertices:

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

Now we can substitute these values into the formula:

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

Calculating each term inside the absolute value:

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

Now, add these results together:

\[
24 + 0 - 4 = 20
\]

Now plug this back into the area formula:

\[
\text{Area} = \frac{1}{2} \left| 20 \right| = \frac{1}{2} \cdot 20 = 10
\]

Therefore, the area of Fiona’s triangle is

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