Transformations of Quadrilateral HRNC Analysis

Quadrilateral HRNC is shown on the coordinate grid.

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Use the drop downs to indicate which of the transformations of quadrilateral HRNC onto H'R'N'C' , preserve distance or not.

Transformation Preserves Distance (x, y) → (3.5x, 3.5y)

(x, y) → (x + 6, y − 2)

(x, y) → (−x , y )

(x, y) → (0.5x, 0.5y)

To determine whether each transformation preserves distance, we need to analyze the nature of each transformation:

1. (x, y) → (3.5x, 3.5y): This transformation is a dilation (scaling) by a factor of 3.5. Dilation does not preserve distance because it changes the size of the figure.

   • Preserves Distance: No

2. (x, y) → (x + 6, y − 2): This transformation is a translation. Translations preserve distance because they move every point the same distance in the same direction without changing the shape or size of the figure.

   • Preserves Distance: Yes

3. (x, y) → (−x, y): This transformation is a reflection across the y-axis. Reflections preserve distance because they maintain the size and shape of the figure, only changing its orientation.

   • Preserves Distance: Yes

4. (x, y) → (0.5x, 0.5y): This transformation is a dilation (scaling) by a factor of 0.5. Like the first transformation, dilation does not preserve distance because it changes the size of the figure.

   • Preserves Distance: No

In summary:

• (x, y) → (3.5x, 3.5y): No
• (x, y) → (x + 6, y − 2): Yes
• (x, y) → (−x, y): Yes
• (x, y) → (0.5x, 0.5y): No