Question

if point (6 1) ( 8,2 ) open (9,4) (x,y) are point of a parallelogram find X and Y​

Answer 1

Answer:

If point (6 1) ( 8,2 ),(9,4) (x,y) are point of a parallelogram then x= 7 and y= 3

Step-by-step explanation:

Let A(6,1), B(8,2), C(9,4) and D(x,y)

We know that the diagonals of a parallelogram bisect each other.  

So, coordinates of the mid-point of diagonal AC are the same as the coordinates of the mid-point of diagonal BD.

$(\frac{6+ 9}{2},\frac{1+4}{2} = (\frac{8 + x}{2}, \frac{2+ y}{2})\\ (\frac{15}{2} ,\frac{5}{2} )= (\frac{8 + x}{2}, \frac{2+ y}{2})\\So, \frac{8 + x}{2} = \frac{15}{2} , \frac{2+ y}{2} = \frac{5}{2}$

2( 8+ x) = 15 (2)

16 + 2x = 30

2x = 30 - 16

2x = 14

x = 7

And 2(2+y) = 5(2)

4 + 2y = 10

2y = 10 - 4

2y = 6

y = 3