Question

What are the four ordered pairs that represent the vertices of a rectangle with a perimeter of 30 units?

A) (5, 10), (10, 5), (5, -10), (10, -5)

B) (8, 7), (7, 8), (-8, -7), (-7, -8)

C) (6, 9), (9, 6), (-6, -9), (-9, -6)

D) (12, 3), (3, 12), (-12, -3), (-3, -12)

Answer 1

The four ordered pairs that represent the vertices of a rectangle with a perimeter of 30 units are (12, 3), (3, 12), (-12, -3), (-3, -12), as only these pairs satisfy the condition where the sum of length and width is 15 and both length and width are positive integers.

Step-by-step explanation:

The question is asking for the four ordered pairs that represent the vertices of a rectangle with a perimeter of 30 units. To find the correct answer, we first acknowledge that the perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where 'l' is the length and 'w' is the width of the rectangle. Thus, for a perimeter of 30 units, we can create the equation 2l + 2w = 30.

By dividing each term by 2, we simplify the equation to l + w = 15. The length and width must be positive integers less than 15 that, when added together, equal to 15, because the question is about a rectangle with integer vertices. Only the ordered pairs in option D satisfy this condition, with the possible combinations being (12, 3) and (3, 12).

Therefore, the vertices of the rectangle that correspond to a rectangle with a perimeter of 30 units will be (12, 3), (3, 12), (-12, -3), (-3, -12).