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Answer :
Final answer:
The given quadrilateral JKLM is a right trapezoid because JK and LM are parallel to each other and perpendicular to KL.
Explanation:
The given quadrilateral JKLM has vertices J(-6,-2), K(6,-6), L(4,-8), and M(-5,-5). We can determine if JKLM is a right trapezoid by analyzing the slopes of its sides. If the slopes of JK and LM are equal and the slopes of KL and JM are negative reciprocals of each other, then JKLM is a right trapezoid.
Using the slope formula, the slope of JK is (y2 - y1)/(x2 - x1) = (-6 - -2)/(6 - -6) = -4/12 = -1/3. The slope of LM is (y2 - y1)/(x2 - x1) = (-8 - -5)/(4 - -5) = -3/9 = -1/3. Since the slopes of JK and LM are equal, JKLM is a right trapezoid. Therefore, the answer is option a. Yes, JK and LM are parallel to each other and perpendicular to KL.
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