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

Answer:

(1,-8)

Step-by-step 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 $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

is $(\frac{-1+5}{2},\frac{-4+-6}{2})=(2,-5)$

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:

$(\frac{3+x}{2},\frac{y+-2}{2})=(2,-5)$

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)