Application of Distance, Midpoint, and Slope — Quiz
Question 5 • Geometry with Statistics
A set of plans for a new bandstand includes a triangular support. The coordinates of the triangle on the plans are A (2,−3) , B (0,−2) , and C (−2,−6) Which statement classifies the triangle by angles?
Answer
A
Since the slope of AB― is negative 1 half and the slope of BC― is 2, the triangle is a right triangle.
B
Since the slope of BC― is 2 and the slope of AC― is 3 fourths, the triangle is an acute triangle.
C
Since the slope of AB― is negative 1 half and the slope of BC― is 2, the triangle is an acute triangle.
D
Since the slope of BC― is 2 and the slope of AC― is 3 fourths, the triangle is a right triangle.
Explanation
The slope of AB is (−2 − (−3))/(0 − 2) = −1/2, and the slope of BC is (−6 − (−2))/(−2 − 0) = 2. These slopes are negative reciprocals, since their product is −1, so AB and BC are perpendicular. Therefore, the triangle is a right triangle, which is choice A.
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