Leonardo draws the obtuse triangle pictured here and calculates the area in square units. What is the area of Leonardo’s triangle? (1 point) Leonardo’s triangle has an area of square units.

Question

Leonardo draws the obtuse triangle pictured here and calculates the area in square units. What is the area of Leonardo’s triangle? (1 point) Leonardo’s triangle has an area of square units.
Point A -5, -4
Point B 3, -3
Point C 3, 2

GPT-4o mini · Answer

To find the area of triangle ABC with vertices A (-5, -4), B (3, -3), and C (3, 2), we can use the formula for the area of a triangle based on the coordinates of its vertices:

$Area = \frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$

Here, let $(x_{1}, y_{1}) = (- 5, - 4)$ , $(x_{2}, y_{2}) = (3, - 3)$ , and $(x_{3}, y_{3}) = (3, 2)$ .

Plugging in the coordinates:

$Area = \frac{1}{2} | (- 5) (- 3 - 2) + (3) (2 - (- 4)) + (3) (- 4 - (- 3)) |$

Calculating each term:

The first term: $(- 5) (- 5) = 25$
The second term: $3 (2 + 4) = 3 (6) = 18$
The third term: $3 (- 4 + 3) = 3 (- 1) = - 3$

Putting these values back into the area formula:

$Area = \frac{1}{2} | 25 + 18 - 3 |$ $= \frac{1}{2} | 40 |$ $= \frac{1}{2} \times 40 = 20$

Thus, the area of Leonardo’s triangle is $20$ square units.