Question

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

Answer 1

Answer:  The value of x = 6 and y = 3.

Step-by-step explanation:

Let ABCD is a parallelogram with vertices  (1,2) ; (4,y) ; (x,6) ; (3,5) respectively.

As we know that

The mid-points of two diagonals must be same.

So, we will apply "Mid point rule":

Mid point of AC is given by

$(\frac{1+x}{2},\frac{2+6}{2})\\\\=(\frac{1+x}{2},4)$

Mid point of BD is given by

$(\frac{4+3}{2},\frac{y+5}{2})\\\\=(\frac{7}{2},\frac{y+5}{2})$

Now, Mid point of AC = Mid point of BD

$(\frac{1+x}{2},4)=(\frac{7}{2},\frac{y+5}{2})\\\\\frac{1+x}{2}=\frac{7}{2}\\\\1+x=7\\\\x=7-1=6\\\\Similarly,\\\\4=\frac{y+5}{2}\\\\8=y+5\\\\y=8-5=3$

Hence, The value of x = 6 and y = 3.