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??

Question

asked Jan 17, 2021 139k views

1 Answer

John Durand · Answer 1 · 2021-01-21T05:19:09+0000

Answer:

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)