Question

A parallelogram ABCD has two vertices at A (1,1) and B (0,7) and its diagonals ​cross at the point (4,3). ​ ​Where are the other two vertices of the ​parallelogram ?

Answer 1

The other two vertices are (7, 5) and (8, -1)

Explanation:

Given,

Two vertices of a parallelogram are A(1,1) and B(0,7)

The diagonals meet at (4,3)

To find the other two vertices of the parallelogram.

We know that the diagonals of a parallelogram intersect each other.

Let, C be the vertex as (x,y)

According to the problem

`(1+x)/(2) = 4 and (1+y)/(2) =3`

or, 1+x = 8 and 1+y = 6

or, x = 7 and y = 5

Again, let D be the vertex as (a,b)

According to the problem,

`(0+a)/(2) = 4 and (7+b)/(2) = 3`

or, a = 8 and 7+b = 6

or, a= 8 and b= -1

Hence the vertices are (7, 5) and (8, -1)