Question

What is the area of the triangle in square units? (1 point) Responses 6 6 15 15 18 18 9
Triangle corner a: (0, 3)
Triangle corner b (10, 6)
triangle corner c: (6, 3)

Answer 1

To find the area of a triangle given its vertices, we can use the formula:

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

where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the coordinates of the triangle's vertices.

Given the vertices of the triangle:
- \(A(0, 3)\)
- \(B(10, 6)\)
- \(C(6, 3)\)

Substituting these coordinates into the formula:

\[
\text{Area} = \frac{1}{2} \left| 0(6-3) + 10(3-3) + 6(3-6) \right|
\]

Calculating each term:

\[
= \frac{1}{2} \left| 0 + 10 \cdot 0 + 6(-3) \right|
\]
\[
= \frac{1}{2} \left| 0 + 0 - 18 \right|
\]
\[
= \frac{1}{2} \left| -18 \right|
\]
\[
= \frac{1}{2} \cdot 18 = 9
\]

Thus, the area of the triangle is \(9\) square units.

Therefore, the answer is \(9\).