Parallelogram question - need help

[onesome]

Question => Two opposite pair of vertices of parallelogram are = (1,1) & (4,4)
If one of the remaining vertices is (m,n), what is the fourth vertex of a parallelogram in terms of m & n ?

A) (1-m, 1-n)
B) (2-m, 3-n)
C) (3-m, 4-n)
D) (m-4, n-4)
E) (5-m, 5-n)


Answer is : E

[ildude02]

We need to use the concept that the diagnols bisect each other to solve this problem. So if you draw diagnols for all the points, the mid point of the diagnoal connecting (4, 4) and (1, 1) is (5/2, 5/2). Now you know that (5/2, 5/2) point is th emid point between (m, n) and (x, y). So you can find (x, y) based on this concept,

m+x / 2 = 5/2; n+x / 2 = 5/2. ;
This will give E for x, y values.

Jus wondering if there is an easier approach?

[onesome]

ildude02 - thanks

I just found this "Mid-point theorem" here and realised this one was simple.

https://www.mathopenref.com/coordmidpoint.html

Thanks again.