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 the triangle with vertices at \((6, 2)\), \((4, 6)\), and \((1, 2)\), we can use the formula for the area of a triangle given 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 coordinates:

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

We can now plug in the values:

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

Calculating the individual terms:

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

Putting it all together:

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

Therefore, the area of Fiona’s triangle is \(\boxed{10}\) square units.