Answer
The area of the triangle = 15 square units.
Step-by-step explanation
To find the area of the triangle, we need to compute the length of the sides of the triangle required to find the area.
The area of a triangle is give as
Area = ½ × Base × Height
The distance between two points with the coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
For the base of the triangle, we calculate the distance between (-2, 2) and (-2, -3)
(x₁, y₁) and (x₂, y₂) is (-2, 2) and (-2, -3) respectively
x₁ = -2
y₁ = 2
x₂ = -2
y₂ = -3
d = √[(-2 - (-2))² + (-3 - 2)²]
d = √[(0)² + (-5)²]
d = √(0 + 25)
d = √25
d = 5 units
For the height of the triangle, we calculate the distance from the coordinates (4, -1) to (-2, -1)
(x₁, y₁) and (x₂, y₂) is (4, -1) and (-2, -1) respectively
x₁ = 4
y₁ = -1
x₂ = -2
y₂ = -1
d = √[(-2 - 4)² + (-1 - (-1))²]
d = √[(-6)² + (0)²]
d = √(36 + 0)
d = √36
d = 6 units
So, the area of the triangle can now be calculated
Base = 5 units
Height = 6 units
Area = ½ × Base × Height
Area = ½ × 5 × 6 = 15 square units.
Hope this Helps!!!