2 in a math contest, the contestants were given the following piecewise graph. For
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Given:
The three vertices of a parallelogram are (-3,8), (4,5), (2,-5).
To find:
The fourth vertex of the parallelogram.
Solution:
Let the vertices of the parallelogram are A(-3,8), B(4,5), C(2,-5) and D(a,b).
We know that, diagonals of a parallelogram bisect each other. It means midpoints of both diagonals are same.
Midpoint formula:
Two diagonals of ABCD are AC and BD.
Midpoint of AC = Midpoint of BD
On comparing both sides, we get
And,
Therefore, the coordinates of fourth vertex are (-5,-2).