Example Solution: A(0,0), B(a+b,0), C(a,c), D(- b,c)
Practice makes perfect
We are asked to name the missing coordinates for the given parallelogram.
Because we are told that the given figure is a parallelogram, we know that AB and DC are parallel. This means that they have the same slope. Let’s use the Slope Formula to calculate the slope of AB.
Slope ofAB: 0- 0/(a+b)- 0 = 0Since the slope of DC must also be 0, there cannot be a change in the y-value between its endpoints. Therefore, we know that the y-coordinate of D is also c.
Moreover, we know that opposite sides are congruent. This means that AB and DC have the same length. Let's calculate AB, the length of AB.
AB: a+b- 0=a+b
Therefore, DC must also be a+b. Let's add the obtained information to our diagram.
We can see above that if we add the x-coordinate of D and the side length a+b, we obtain the x-coordinate of C. Let - b be the x-coordinate of D.
x-coordinate ofC: - b+a+b=a
We found that possible coordinates for the given parallelogram are A( 0, 0), B( a+b, 0), C(a, c), and D(- b, c).
Note that this is just one possible solution. Other coordinates also make the figure a parallelogram.
