We are asked to name the missing coordinates for the given parallelogram. In the given diagram, we can see that X is on the x-axis. Therefore, its y-coordinate is 0.
Because we are told that the given figure is a parallelogram, we know that ZY and WX are parallel. This means that they have the same slope. Let’s use the Slope Formula to calculate the slope of WX.
Slope ofWX: 0- 0/a- 0 =
Since the slope of ZY must also be , there cannot be a change in the y-value between its endpoints. Therefore, we know that the y-coordinate of Y is also c.
Moreover, we know that opposite sides are congruent. This means that ZY and WX have the same length. Let's calculate WX, the length of WX.
WX: a- 0=a
Therefore, ZY must also be a. Let's add the obtained information to our diagram.
We can see above that if we add the x-coordinate of Z, which is - b, and the side length a, we obtain the x-coordinate of Y.
x-coordinate ofY: - b+a=a-b
We found that possible coordinates for the given parallelogram are W( 0, 0), X( a, 0), Y(a-b, c), and Z( - b, c).
