Final answer:
The student's question is about finding the perimeter of a rectangle given the coordinates of two of its corners. The best-educated guess for the perimeter is 32 units since it is the only one that provides a whole number for the width when halved.
Step-by-step explanation:
The question provided involves calculating the perimeter of a rectangle given the coordinates of its upper corners. The coordinates of the upper-left corner are (-6, 6), and the upper-right corner are (1, 6). Because both points have the same y-coordinate, they are on the same horizontal line, and the difference in the x-coordinates gives us the length of the top side of the rectangle. The length is the absolute value of the difference between -6 and 1, which is 7 units. Since a rectangle has two sides of equal length, the total length contribution to the perimeter is twice this, which is 14 units.
To calculate the perimeter, we also need the width of the rectangle. We know the perimeter is the sum of all four sides. However, we do not have the coordinates for the bottom corners, which prevent us from directly calculating the width. Yet, we are given multiple choice answers for the perimeter. Since we already have calculated the total length as 14 units, the remaining perimeter should be twice the width (because a rectangle has two sides of equal width). By subtracting 14 from each of the answer choices, we can find the width and consequently determine if the widths are the same for any two choices (only single values for the length and the width would suggest a possible correct perimeter). Here are the calculations:
- 28 units - 14 units = 14 units, so width would be 7 units.
- 32 units - 14 units = 18 units, so width would be 9 units.
- 26 units - 14 units = 12 units, so width would be 6 units.
- 30 units - 14 units = 16 units, so width would be 8 units.
Among the given options, the only possible perimeter that would allow both length and width to be whole numbers is 32 units because none of the other perimeters provide an even number when halved. So, the correct answer is (b) 32 units. It's important to note that a comprehensive answer would require knowledge about the rectangle's width, but given the limitations and the multiple choice format, we are making an educated guess based on the need for the sides to be whole numbers.