23. If (1, 2), (4,y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in ,
order then find x and y

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