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Difficulty: EasyGeometric Figures on the Coordinate Plane

In the standard (x,y)(x,y) coordinate plane, a rectangle has vertices at (−2,−3)(-2, -3), (4,−3)(4, -3), (4,2)(4, 2), and (−2,2)(-2, 2). What is the area, in square units, of this rectangle?

Answer: 30 square units

Answer

The area of the rectangle is 30 square units.
The area of a rectangle is the product of its length and width. By finding the difference between the x-coordinates of the horizontal vertices (4−(−2)=64 - (-2) = 6) and the difference between the y-coordinates of the vertical vertices (2−(−3)=52 - (-3) = 5), we find the dimensions to be 6 and 5. Multiplying these gives 6×5=306 \times 5 = 30.

Step-by-Step Solution

1
Determine the length of the horizontal sides of the rectangle.
The horizontal sides have a length of 6 units.
The horizontal sides connect vertices with the same y-coordinates, such as (−2,−3)(-2, -3) and (4,−3)(4, -3). The distance is the difference in their x-coordinates: 4−(−2)=64 - (-2) = 6.
2
Determine the length of the vertical sides of the rectangle.
The vertical sides have a length of 5 units.
The vertical sides connect vertices with the same x-coordinates, such as (4,−3)(4, -3) and (4,2)(4, 2). The distance is the difference in their y-coordinates: 2−(−3)=52 - (-3) = 5.
3
Calculate the area of the rectangle.
The area of the rectangle is 30 square units.
The area of a rectangle is found by multiplying its length by its width: Area=6×5=30\text{Area} = 6 \times 5 = 30.

Key Concept

Finding the area of a rectangle on the coordinate plane by calculating the lengths of its horizontal and vertical sides.
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Topics

Geometric Figures on the Coordinate Plane

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