/ Three vertices of parallelogram ACBE are shown. Find the coordinates of vertex
e. (Hint: Pay attention to the order in which the parallelogram is named.)
a. (–2, 4)
b. (8, 9)
c. (-2, 5)
d. (3, 0)
We have to find the coordinates of vertex E of parallelogram ACBE. First
we have to find the midpoint of a diagonal AB : xM = ( xA + xB ) / 2 = (
1 + 3 ) / 2 = 4 /2 = 2; yM = ( yA + yB ) / 2 = ( 2 + 6 ) / 2 = 8 / 2 =
4. So the coordinates of the midpoint are M ( 2, 4 ). And it is also a
midpoint of another diagomal ( CE ). ( xE + 6 ) / 2 = 2; xE + 6 = 4; xE
= 4 - 6 = - 2. ( yE + 4 ) / 2 = 4; yE + 4 = 8; yE = 8 - 4 = 4.
Answer: The coordinates of vertex E are A ) ( -2, 4 ).
