Detail of question with options is in the picture. Relevance

RectangleABCD has vertices A(4, 5), B(0, 2), and C(6, -6).

What are the coordinates of vertex D?

Justify the answer with an explanation.

The answer is E. (2, - 9)

x and y coordinates of A and B differ by 4 and 3 respectively.

Subtracting these from the x and y coordinates of C

gives the coordinate of point D.

• Consider ln L through C(6,-6) // to BA. Slope BA = (5-2)/(4-0) =(3/4). Suppose D(x,y)

is the 4th vertice. We would then require slope DC = slope BA = (3/4) = (-6-y)/(6-x).

Then -6-y = 3 & 6-x = 4, ie., x = 2 & y = -9. Then D = (2,-9). For D' = (10,-3) we can also demonstrate that D' is a legitimate location for the 4th vertice. Instead of going

from C  4 to the left & down 3 getting to D(2,-9), we can go 4 to the right  & up 3

getting to D'(10,-3). Comparing slopes involving D with slopes involving D' we can

prove that rectangles ABCD and ABCD' are both legitimate rectangles.

• You know how a rectangle looks. From B to A is 4 right and 3 up so from C to D will be 4 right and 3 up.