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Parallelogram ABCD has A(0, 1), B(2, 1) and C(4, 0) as three of its vertices. What is the sum of the coordinates of point D?

 Jun 1, 2020
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Line AB is horizontal. We know that parallelograms have two sets of parallel sides, meaning line CD will also be horizontal, or have a slope of 0.

 

Next we need to find the slope of line BC, which would be -1/2. That would be parallel to AD.

 

Point D will be the solution of line CD and AD. The equations for those two lines are:

 

y=-1/2x+1

y=0

 

Now substitute.

 

0=-1/2x+1

-1=-1/2x

2=x

 

So we take x=2 and y=0 to get the coordinates (2,0).

 

2+0=2

 Jun 1, 2020
edited by lovelyy.riss  Jun 1, 2020

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