Question

IF A(4, -1), B(5, 3), C(2,y) and D(1, 1) are the vertices of a

parallelogram ABCD, find y.​

Answer 1

Answer:

y=5,-3

Step-by-step explanation:

We know that if ABCD is a parallelogram then :

AB=CD

Square on both sides

AB²=CD²

(5-1)²+(3-(-1))²=(2-1)²+(y-1)²

1+16=1+y²+1-2y

17=2+y²-2y

0=y²-2y-15

0=y²-5y+3y-15

0=y(y-5)+3(y-5)

0=(y-5)(y+3)

If y-5=0 then y=5

If y+3=0 then y=-3