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A coordinate plane shows both axes ranging from negative 2 to 8 in increments of 1. Four labeled points are plotted and joined to form a rectangle. The four points are labeled as upper A, upper B, upper C, and upper D, respectively, and are plotted at coordinates left parenthesis 1 comma 0 right parenthesis, left parenthesis 1 comma 3 right parenthesis, left parenthesis 5 comma 3 right parenthesis, and left parenthesis 5 comma 0 right parenthesis, respectively. All four points are connected by solid lines to form a rectangle. The area inside the rectangle is shaded.

Chris and Oscar bought a new television for their mom. They want to be sure it will fit on the wall, so they need to calculate the perimeter of the television. Use the graph to help them calculate the perimeter of the television.

1 answer

To find the perimeter of the rectangle formed by the points A, B, C, and D, we first identify the coordinates of each point:

  • A: (1, 0)
  • B: (1, 3)
  • C: (5, 3)
  • D: (5, 0)

Next, we calculate the lengths of the sides of the rectangle. The rectangle's sides are vertical and horizontal:

  1. The length of the vertical sides (A to B and D to C) can be calculated by finding the difference between the y-coordinates of the points:

    • Distance between A (1, 0) and B (1, 3) is \( 3 - 0 = 3 \).

  2. The length of the horizontal sides (B to C and A to D) can be calculated by finding the difference between the x-coordinates of the points:

    • Distance between A (1, 0) and D (5, 0) is \( 5 - 1 = 4 \).

Now, we have:

  • The length of the vertical sides: \( 3 \)
  • The length of the horizontal sides: \( 4 \)

To calculate the perimeter \( P \) of the rectangle, we use the formula: \[ P = 2 \times ( \text{length} + \text{width} ) \] Substituting the values we calculated: \[ P = 2 \times (4 + 3) = 2 \times 7 = 14 \]

Therefore, the perimeter of the rectangle is \( 14 \) units.