Final answer:
The area of a triangle with vertices (4, -4), (5, -4), and (3, 3) is calculated using the 1/2 × base × height formula. The base is 1 unit in length, and the height is 7 units, leading to an area of 3.5 square units, which is then rounded to 4 square units.
Step-by-step explanation:
To find the area of a triangle with given vertices, we can use the formula 1/2 × base × height. First, we should identify the base and height of the triangle which can be done by looking at the coordinates of the vertices. The vertices given are (4, -4), (5, -4), and (3, 3).
Notice that the two points (4, -4) and (5, -4) form a horizontal line segment and thus can be used as the base of the triangle. The length of the base is the difference between the x-coordinates of these two points which is |5 - 4| = 1 unit.
To find the height, we look for the vertical distance between the base and the opposite vertex (3, 3). Since our base is at y = -4, and the y-coordinate of the opposite vertex is 3, the height is |3 - (-4)| = 7 units.
Now that we have the base and the height, we can apply the formula for the area of a triangle:
Area = 1/2 × base × height
Area = 1/2 × 1 × 7
Area = 1/2 × 7
Area = 3.5
Since the area is asked to be rounded to the nearest square unit, the area of the triangle is approximately 4 square units.