
Concept explainers
Whether the figure with given vertices is a trapezoid.

Answer to Problem 13PPS
JKLM is a trapezoid.
The lengths are not equal, hence JKLM is not an isosceles trapezoid.
Explanation of Solution
Given:
The given vertices are:
Calculation:
Draw the quadrilateral using given vertices:
A trapezoid has exactly one pair of opposite sides.
Use the slope formula to compare the opposite sides:
The slope of JK will be:
The slope of KL will be:
The slope of LM will be:
The slope of MJ will be:
The slopes of exactly one pair of opposite sides are equal, so exactly one pair of opposite sides is parallel.
Hence, JKLM is a trapezoid.
Now, apply the Distance Formula to compare the lengths:
The length of KL will be:
The length of JM will be:
The lengths are not equal, hence JKLM is not an isosceles trapezoid.
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