Final answer:
The correct rectangle with side lengths of 5 units and 6 units, from the given options, is (c) with vertices A(1,2), B(1,8), C(6,8), D(6,2).
Step-by-step explanation:
The student asks which rectangle has side lengths of 5 units and 6 units from a list of given coordinates for rectangles. To determine the correct rectangle, one would check the differences in the x-coordinates and y-coordinates for adjacent vertices. In this case, options (a), (b), (c), and (d) represent various rectangles with their vertices labeled as A, B, C, and D. Since the difference in x-coordinates or y-coordinates can represent the lengths of the sides of the rectangle, we can calculate these differences for each option to find the rectangle with the side lengths that match 5 units and 6 units.
For option (a), the rectangle would have side lengths of AB (y-coordinates differ by 5) and BC (x-coordinates differ by 5), so it doesn't match the required side lengths. In option (b), AB has a length of 6 and BC has a length of 6, which is also incorrect. Option (c) has the lengths of AB as 6 (since 8 - 2 = 6) and BC as 5 (since 6 - 1 = 5), making it a potential match. Lastly, option (d) has lengths of AB as 4 and BC as 5, which is incorrect.
Upon analyzing all options, the correct rectangle is option (c), with vertices A(1,2), B(1,8), C(6,8), D(6,2), as it is the only one with side lengths of 6 units and 5 units corresponding to 5 units wide (horizontal) and 6 units tall (vertical).