Answer:
Below
Step-by-step explanation:
To prove that the diagonals bisect each other we should prove that they have a common point.
From the graph we notice that this point is E.
ABCD is a paralellogram, so E is the midpoint of both diagonals.
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Let's start with AC.
● A(0,0)
● C(2a+2b,2c)
● E( (2a+2b+0)/2 , (2c+0)/2)
● E ( a+b, c)
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BD:
● B(2b,2c)
● D(2a,0)
● E ( (2a+2b)/2 , 2c/2)
● E ( a+b ,c)
●●●●●●●●●●●●●●●●●●●●●●●●●
So we conclude that the diagonals bisect each others in E.
