Finding remaining co-ordinate of a parallelogram

Question

You have 2 [(x1,y1) & (x2,y2)] co ordinates of a parallelogram and the length of the two different base(ab,cd). What is the co-ordinate of the remaining points?

Answer 1

You have two coordinates of a parallelogram (x1, y1) and (x2, y2)

and

you have two side lengths ab and CD, adjoining sides

what are the coordinates of the remaining 2 points??

take a more specific example, then generalize

let the 2 points be (1,2) and (2,6) with ab = 1 and cd = sqr10

then the remaining 2 points are (2,1) and (3,6)

Generalize 1 =x1, 2=y1, 2=x2, 6=y2,

remaining 2 points have 2 = x3, 2=y3, 3=x4, 6=y4

to get to x3, double x2, to get y3 just set y3=y1

to get x4 multiply x2 times 3/2, to get y4 let y4=y2