Question

if (1,2) (4,y) (x,6) and (3,5) are the vertices of a parallelogram taken in order. find xand y

Answer 1

LetA = (1,2), B = (4, y), C= (x, 6) and D= (3, 5)

We know that diagonals of parallelogram bisect each other. It means that coordinates of midpoint of diagonalACwould be same as coordinates of midpoint of diagonalBD------(1)

UsingSection formula, the coordinates of midpoint ofACare:

(1+x2,(2+6)2)=((1+x)2,4)

Using Section formula, the coordinates of midpoint ofBDare:

((4+3)2,(5+y)2)=(72,(5+y)2)

According to condition(1),we have(1+x)2=72

⇒(1+x)=7

⇒x=6

According to condition(1),we also have4=5+y2

⇒8=5+y

⇒y=3

Therefore,x=6andy=3