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:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

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

Midpoint of AC = Midpoint of BD

$\left(\dfrac{0+(-1)}{2},\dfrac{6+(-5)}{2}\right)=\left(\dfrac{5+a}{2},\dfrac{-4+b}{2}\right)$

$\left(\dfrac{-1}{2},\dfrac{1}{2}\right)=\left(\dfrac{5+a}{2},\dfrac{-4+b}{2}\right)$

On comparing both sides, we get

$\dfrac{5+a}{2}=-\dfrac{1}{2}$

$5+a=-1$

$a=-1-5$

$a=-6$

And,

$\dfrac{-4+b}{2}=\dfrac{1}{2}$

$-4+b=1$

$b=1+4$

$b=5$

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