Final answer:
After calculating the dimensions of the rectangle using the given perimeter and coordinates of the top corners, the coordinates of the lower-left corner are found to be (-6, -2). There seems to be a problem with the question as this answer does not match any of the provided options.
Step-by-step explanation:
The student asked what the coordinates of the lower-left corner of a rectangle are, given that the upper-left corner is at (-6,6), the upper-right corner is at (1,6), and the perimeter is 30 units. To find the coordinates of the lower-left corner, we need to use the properties of a rectangle and the given perimeter to determine the rectangle's dimensions.
Firstly, to find the length of the top side, we calculate the distance between the upper-left and the upper-right coordinates:
Length = x2 - x1 = 1 - (-6) = 7 units.
Since the opposite sides of a rectangle are equal, we have two sides of the rectangle that are 7 units long. The perimeter of a rectangle is 2 times the length plus 2 times the width (P = 2l + 2w). The given perimeter is 30 units, so:
30 = 2(7) + 2w
Next, we solve for the width (w):
30 = 14 + 2w => 2w = 16 => w = 8 units.
The width corresponds to the vertical sides of the rectangle. The y-coordinate of the lower-left corner thus will be the y-coordinate of the upper-left corner minus the width: ynew = 6 - 8 = -2.
So, the coordinates of the lower-left corner are (-6, -2), which matches none of the provided option (a) through (d). It seems there is an error in the question if the correct answer is not among the choices given.