Questions: 20. Which figure has exactly one line of symmetry? A. Figure I B. Figure II C. Figure III

20. Which figure has exactly one line of symmetry? A. Figure I B. Figure II C. Figure III
Transcript text: 20. Which figure has exactly one line of symmetry? A. Figure I B. Figure II C. Figure III
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Solution

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Solution Steps

Step 1: Identify the figure with exactly one line of symmetry
  • Figure I: A square has four lines of symmetry.
  • Figure II: A parallelogram has no lines of symmetry.
  • Figure III: An isosceles triangle has one line of symmetry.
  • Figure IV: A trapezoid has one line of symmetry.

Answer: Figure III

Step 2: Reflect the triangle over the x-axis

Given vertices:

  • \( G(0, -2) \)
  • \( Y(-3, 0) \)
  • \( M(-3, -4) \)

Reflecting over the x-axis:

  • \( G'(0, 2) \)
  • \( Y'(-3, 0) \) (no change as it lies on the x-axis)
  • \( M'(-3, 4) \)
Step 3: Rotate the triangle 90° clockwise

Using the reflected coordinates:

  • \( G'(0, 2) \)
  • \( Y'(-3, 0) \)
  • \( M'(-3, 4) \)

Rotating 90° clockwise:

  • \( G''(2, 0) \)
  • \( Y''(0, 3) \)
  • \( M''(4, 3) \)

Final Answer

  1. Figure with exactly one line of symmetry: Figure III
  2. Reflected coordinates over the x-axis:
    • \( G'(0, 2) \)
    • \( Y'(-3, 0) \)
    • \( M'(-3, 4) \)
  3. Rotated coordinates 90° clockwise:
    • \( G''(2, 0) \)
    • \( Y''(0, 3) \)
    • \( M''(4, 3) \)
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