Prove that a quadrilateral is a parallelogram.
Answer to Problem 4CFU
Explanation of Solution
Given information:
The coordinates of the vertices.
Calculation:
Here, we will consider
Now, we will consider
Now, distance between the point
Now, distance between the point
Therefore,
Now, distance between the point
Now, distance between the point
Therefore,
Thus,
Now, we will consider
Now, mid-point of diagonal
Now, mid-point of diagonal
Here, we can see that two diagonals bisect each other. Thus,
Now, we will consider
From
Slope of side
Slope of side
Therefore, opposite sides are parallel. Thus,
Now, we will consider
From
Now, provided
Thus,
Hence, the results are shown above.
Chapter 10 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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