Question

Three vertices of parallelogram WXYZ are W(3,1), X(2,7),and Z(4,0). How do I find the coordinates of vertex Y?

How do I find the other coordinate?

Answer 1

`(3,6) and (1,8)`

Explanation:

Some of the properties of a parallelogram:
a) Opposite sides are parallel.
b) Opposite sides are congruent.
c) Opposite angles are congruent.
d) The diagonals bisect each other, `=>` the two diagonals have the same midpoint.

The Midpoint Formula: The midpoint of two points, `(x_1, y_1)` and `(x_2, y2)` is the point M found by the following formula :

`M=((x_1+x_2)/2, (y_1+y_2)/2)`

First, let `XZ and WY` be the two diagonals,
`=> XZ and WY` have the same midpoint,

`=> (2+4)/2=(3+x)/2, => x=3`
`=> (7+0)/2=(1+y)/2, => y=6`

Hence, the first coordinates of vertex `Y` are `(3,6)`

Then, let `XW and YZ` be the two diagonals,
`=> XW and YZ` have the same midpoint.

`=> (2+3)/2=(x+4)/2, => x=1`
`=> (7+1)/2=(y+0)/2, => y=8`

So the second coordinates for vertex Y are `(1,8)`

Hence, the two possible coordinates for vertex Y are `(3,6) and (1,8)`