Final answer:
To find the area of the triangle with vertices at (-2, 0), (4, 0), and (1, 5), calculate 1/2 times the base times the height. The base is 6 units, and the height is 5 units. Thus, the area is 15 square units.
Step-by-step explanation:
The question asks to calculate the area of a triangle with vertices at (-2, 0), (4, 0), and (1, 5) in the coordinate plane. To determine the area, we can use the formula for the area of a triangle on a coordinate plane which is 1/2 × base × height.
In this case, the base can be taken as the distance between the points (-2, 0) and (4, 0), which is 6 units. The height can be taken as the distance from either of these points to the point (1, 5), which is 5 units. Plugging these into the area formula, we get:
Area = 1/2 × base × height
= 1/2 × 6 × 5
= 3 × 5
= 15 square units
So, the area of the triangle is 15 square units.
Answer: a) 15 square units