Question

Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex. xy , 3−2 , −1−4 , 5−6

Answer 1

(1,-8)

Explanation:

We were given three vertices of a parallelogram to be:

(3,-2), (-1,-4), (5,-6).

After plotting the points as shown in the attachment, we realize (3,-2) and (-1,-4) form a diagonal.

The midpoint of this diagonal using the midpoint formula is
`((x_1+x_2)/(2),(y_1+y_2)/(2))`

is
`((-1+5)/(2),(-4+-6)/(2))=(2,-5)`

Recall that, the midpoint of both diagonals are the same.

Let the fourth point have coordinates (x,y).

Then using the midpoint formula again with (3,-2), we have:

`((3+x)/(2),(y+-2)/(2))=(2,-5)`

This implies that:

`x+3=4` and
`y-2=-10`

`x=4-3` and
`y=-10+2`

x=1 and y=-8

The coordinates of the fourth point are:

(1,-8)