Examkin

Question

Difficulty: EasyGeometric Figures on the Coordinate Plane

A rectangle has vertices at A(−1,−2)A(-1, -2), B(3,−2)B(3, -2), C(3,1)C(3, 1), and D(−1,1)D(-1, 1) in the standard (x,y)(x,y) coordinate plane. What is the perimeter of this rectangle?

  1. A
    7
  2. B
    10
  3. C
    11
  4. D
    12
  5. 14Answer

Answer

14
The horizontal length of the rectangle is 3−(−1)=43 - (-1) = 4 units, and the vertical length is 1−(−2)=31 - (-2) = 3 units. Using the formula for the perimeter of a rectangle, P=2(width+height)P = 2(\text{width} + \text{height}), we get P=2(4+3)=14P = 2(4 + 3) = 14 units.

Step-by-Step Solution

1
Calculate the horizontal length (width) of the rectangle.
width = 4
Since vertices A(−1,−2)A(-1, -2) and B(3,−2)B(3, -2) share the same y-coordinate, the horizontal distance between them is the difference in their x-coordinates: 3−(−1)=43 - (-1) = 4.
2
Calculate the vertical length (height) of the rectangle.
height = 3
Since vertices B(3,−2)B(3, -2) and C(3,1)C(3, 1) share the same x-coordinate, the vertical distance between them is the difference in their y-coordinates: 1−(−2)=31 - (-2) = 3.
3
Use the perimeter formula for a rectangle to find the total perimeter.
perimeter = 14
The perimeter is given by P=2(width+height)=2(4+3)=2(7)=14P = 2(\text{width} + \text{height}) = 2(4 + 3) = 2(7) = 14.

Key Concept

Perimeter of geometric figures on the coordinate plane
Estimated Time:45s
Rate this question

Topics

Geometric Figures on the Coordinate Plane

More questions from this topic