Question

On a coordinate plane, the location of 3 points are: (0, 6). (5. -4), and (-1-5). Where would the fourth point need to be located in order to form a parallelogram?

Answer 1

Given:

The three vertices of parallelogram are (0,6),(5,-4),(-1,-5).

To find:

The fourth vertex of the parallelogram.

Solution:

Consider the given vertices of parallelogram are A(0,6), B(5,-4), C(-1,-5).

Let the fourth vertex be D(a,b).

Midpoint formula:

`Midpoint=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

We know that the diagonal of parallelogram bisect each other. It means their midpoints are same.

Midpoint of AC = Midpoint of BD

`\left((0+(-1))/(2),(6+(-5))/(2)\right)=\left((5+a)/(2),(-4+b)/(2)\right)`

`\left((-1)/(2),(1)/(2)\right)=\left((5+a)/(2),(-4+b)/(2)\right)`

On comparing both sides, we get

`(5+a)/(2)=-(1)/(2)`

`5+a=-1`

`a=-1-5`

`a=-6`

And,

`(-4+b)/(2)=(1)/(2)`

`-4+b=1`

`b=1+4`

`b=5`

Therefore, the coordinates of fourth vertex are (-6,5).