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A triangle is graphed by joining three plotted points on the first quadrant of a coordinate plane. The x and y axes range from 0 to 10 in increments of 2.

What is the area of the triangle in square units?

Responses

9
9 - not selected, this is the correct answer

18
18 - no response given

15
15 - incorrect

6
6 - no response given
The coordinates are A (0,3) c is (6,3) B is (10,6)
the correct answer is 9
in 5-6 sentences explai how you can get 9 for the answer

3 answers

To find the area of triangle ABC with vertices at A (0,3), B (10,6), and C (6,3), we can use the formula for the area of a triangle given by coordinates. The formula is:

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

Substituting the coordinates into the formula:

  • \( (x_1, y_1) = (0, 3) \)
  • \( (x_2, y_2) = (10, 6) \)
  • \( (x_3, y_3) = (6, 3) \)

We calculate as follows:

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

This simplifies to:

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

Therefore, the area of triangle ABC is 9 square units. This calculation confirms that the answer is indeed 9.

in simple and shorter terms

To find the area of triangle ABC with vertices A (0,3), B (10,6), and C (6,3), we can use the area formula for coordinates:

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

Plugging in the points:

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

This simplifies to:

\[ = \frac{1}{2} \left| 0 + 0 - 18 \right| = \frac{1}{2} \times 18 = 9 \]

Thus, the area of the triangle is 9 square units.