Question

The coordinates of three of the vertices of rectangle ABCD are A(2,1), B(5,1),and C(5,6). What are the coordinates of point D??

Answer 1

Explanation:

+ The 2 diagonals AC et BD have their midpoint M.

+ We can find M like:

`x_(M)=(x_(A)+x_(C) )/(2) = (2+5)/(2) =7/2\\\\ y_(M)=(y_(A)+y_(C) )/(2) = (1+6)/(2) =7/2\\`

So, we can find D like:

`x_{D =2x_(M) -x_(B) = 2*(7/2) - 5 = 7 - 5= 2\\\y_(D) = 2y_(M) -y_(B) = 2*(7/2) - 1 = 7 - 1= 6\\`

The answer is D(2,6)