Question

If A(4,-1) B(5,3) C(2,y) and D(1,1) are the vertices of the parallelogram ABCD then find y

Answer 1

the correct solution of the given question

Answer 2

Answer:

Value of y is 5.

Step-by-step explanation:

Given  A(4,-1) B(5,3) C(2,y) and D(1,1) are the vertices of the parallelogram ABCD. we have to find the value of y.

As diagonal of parallelogram bisect each other.

Hence, X is the mid-point of AC as well as BD.

By mid-point formula,

If A(a,b) and B(c,d) are two end points of line segment, then the mid-point of AB is $(\frac{a+b}{2},\frac{c+d}{2})$

Since X is the mid-point of AC as well as BD.

⇒ $(\frac{1+5}{2},\frac{1+3}{2})=(\frac{4+2}{2},\frac{-1+y}{2})$

⇒ $(3,2)=(3,\frac{-1+y}{2})$

Comparing both sides

$\frac{-1+y}{2}=2$

⇒ -1+y=4 ⇒ y=5

Hence, value of y is 5