The area of the rectangle is 60 units²
Since from the graph, we have the vertices of the rectangle at (-1,1), (8, -2), (-3, -5) and (6, -8).
The pair (-1, 1) and (8, -2) represent the coordinates for the length of the rectangle while the pair (-1, 1) and (-3, -5) represent the coordinates for the width of the rectangle.
So, we find the length of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₂, y₂)
So, the length, L = √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) = (-1, 1) and (x₂, y₂) = (8, -2)
So, L = √[(x₂ - x₁)² + (y₂ - y₁)²]
L = √[(8 - (-1))² + (-2 - 1)²]
L = √[(8 + 1))² + (-3)²]
L = √[(9)² + (-3)²]
L = √[81 + 9]
L = √90
L = 3√10 units
Also, we find the width of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₃, y₃)
So, the width, W = √[(x₃ - x₁)² + (y₃ - y₁)²] where (x₁, y₁) = (-1, 1) and (x₃, y₃) = (-3, -5)
So, W = √[(x₃ - x₁)² + (y₃ - y₁)²]
W = √[(-3 - (-1))² + (-5 - 1)²]
W = √[(-3 + 1))² + (-6)²]
W = √[(-2)² + (-6)²]
W = √[4 + 36]
W = √40
W = 2√10 units
Since the area of a rectangle A = LW, we have
A = 3√10 units × 2√10 units
A = 3 × 2 × √10 × √10 units²
A = 3 × 2 × 10 units²
A = 60 units²
So, the area of the rectangle is 60 units²
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