Answer:
x = 6 and y = 3
Step-by-step explanation:
A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.
Hence for parallelogram with vertices at A(1, 2), B(4,y), C(x, 6) and D(3, 5)
Let O be the midpoint of the diagonal AC and O be the midpoint of diagonal BD, hence:
For AC:
x coordinate of O = (x + 1) / 2
y coordinate of O = (6 + 2) / 2 = 8/2 = 4
The coordinate of O is [(x + 1)/2, 4]
For BD:
x coordinate of O = (3 + 4) / 2 = 7/2
y coordinate of O = (y + 5) / 2
The coordinate of O is [7/2, (y + 5) / 2 ]
Therefore: [(x + 1)/2, 4] = [7/2, (y + 5) / 2 ]
(x + 1)/2 = 7/2 and (y + 5) / 2 = 4
x + 1 = 7, and y + 5 = 8
x = 7 - 1 and y = 8 - 5
x = 6 and y = 3
