Question

30. If (3,3), (6, )(, 7) and (5,6) are the vertices of a
parallelogram taken in order, find x and y.

Answer 1

Answer:

x=8,y=4

Step-by-step explanation:

Let A(3,3), B(6,y), C(x,7), D(5,6) be the vertices of a parallelogram taken in order,

Diagonals of a parallelogram bisect each other

∴ MidPoint of AC = Mid Point of BD

Mid-point of AC:

x-coordinate =

$\frac{3 + x}{2}$

y-cooordinate =

$\frac{3 + 7}{2}$

Mid point of BD:

x-coordinate=

$\frac{5 + 6}{2}$

y-coordinate=

$\frac{6 + y}{2}$

x-coordinate of the midpoint of AC = x-coordinate of the midpoint of BD

$\frac{3 + x}{2} = \frac{11}{2}$

=> 6+2x=22

=> 2x=16

=>x=8

y-coordinate of midpoint of AC = y-coordinate of midpoint of BD

$5 = \frac{6 + y}{2}$

=> 10= 6+y

=>4=y