Praxis 5003 Practice Test Practice Question
A right triangle is drawn in the xy-plane. The vertex of the right angle is located at the point (-8,2), and another vertex is located at the point (-8,5). One leg of the triangle is parallel to the x-axis and has a length that is three times the length of the other leg of the triangle. Which of the following could be the location of the third vertex?
Correct Answer: A
Rationale: To determine the location of the third vertex of the right triangle, we first note that one leg is vertical (from (-8,2) to (-8,5)), and its length is 3 units. The horizontal leg must then be 1 unit long since it is three times shorter. The horizontal leg can extend either left or right from the vertex at (-8,2).
Option A (1,2) is valid as it lies 9 units to the right on the same horizontal line as (-8,2), forming the necessary right triangle.
Option B (1,5) is incorrect because it does not maintain the right angle since it connects to the vertical leg, violating the triangle's properties.
Options C (-7,2) and D (-7,5) also fail since they do not create a leg that is three times the length of the other leg, which is required for the triangle's proportions.
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