Question 390086: if three vertices of the parallelogram are A(2,0), B(4,4),C(6,0),find the fourth vertex D if D is in the 4th quadrant
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785)   (Show Source):
Answer by Edwin McCravy(20059)  (Show Source):
You can put this solution on YOUR website! if three vertices of the parallelogram are A(2,0), B(4,4),C(6,0),find the fourth vertex D if D is in the 4th quadrant
Draw AB and BC:
To have a parallelogram with the fourth vertex in the fourth quadrant, by
symmetry, D has to be as far below the x-axis as B is above it. So it has
to be like the x-axis was a reflection pool and the rest of the parallelogram
is it's reflection "down in the water" or the fourth quadrant.
So D has to be D(4,-4), the reflection of B(4,4). The resulting parallelogram
is a special kind where all four sides have the same length, and is called
a "rhombus"
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