Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question
**Problem Statement:** Given the graph of triangle \( \Delta XYZ \) with the coordinates \( X(1, 3) \), \( Y(4, -1) \), and \( Z(5, 6) \), determine which statement proves that \( \Delta XYZ \) is an isosceles right triangle. **Graph Description:** The graph represents a coordinate plane with triangle \( \Delta XYZ \) plotted. The vertices \( X \), \( Y \), and \( Z \) are labeled: - \( X(1, 3) \) - \( Y(4, -1) \) - \( Z(5, 6) \) **Task:** Select the correct statement that proves \( \Delta XYZ \) is an isosceles right triangle from the following options: 1. \( XZ \perp XY \) 2. \( XZ = XY = 5 \) 3. The slope of \( XZ \) is \( \frac{3}{4} \), the slope of \( XY \) is \( -\frac{4}{3} \), and \( XZ = XY = 5 \) 4. The slope of \( XZ \) is \( \frac{3}{4} \), the slope of \( XY \) is \( -\frac{4}{3} \), and the slope of \( ZY \) is 7 **Options:** - Mark this and return - Save and Exit - Next - Submit
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Transcribed Image Text:**Problem Statement:** Given the graph of triangle \( \Delta XYZ \) with the coordinates \( X(1, 3) \), \( Y(4, -1) \), and \( Z(5, 6) \), determine which statement proves that \( \Delta XYZ \) is an isosceles right triangle. **Graph Description:** The graph represents a coordinate plane with triangle \( \Delta XYZ \) plotted. The vertices \( X \), \( Y \), and \( Z \) are labeled: - \( X(1, 3) \) - \( Y(4, -1) \) - \( Z(5, 6) \) **Task:** Select the correct statement that proves \( \Delta XYZ \) is an isosceles right triangle from the following options: 1. \( XZ \perp XY \) 2. \( XZ = XY = 5 \) 3. The slope of \( XZ \) is \( \frac{3}{4} \), the slope of \( XY \) is \( -\frac{4}{3} \), and \( XZ = XY = 5 \) 4. The slope of \( XZ \) is \( \frac{3}{4} \), the slope of \( XY \) is \( -\frac{4}{3} \), and the slope of \( ZY \) is 7 **Options:** - Mark this and return - Save and Exit - Next - Submit
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