QuestionJUSTIFY REASONING Consider the statement: If is a real number, then a dilation centered at the origin maps the line to itself. Which statement best determines whether the statement is sometimes, always, or never true and justifies the reasoning? A) Sometimes; The line passes through the origin, but depending on the value of , the image may map onto itself or may be parallel or perpendicular and not map onto itself. B) Always; The line passes through the origin and a dilation leaves lines through the center of dilation unchanged. C) Sometimes; The line passes through the origin, but if is negative, the dilation would be perpendicular to the preimage. D) Never; The line passes through the origin and because the origin is the center of dilation, the image line will be parallel to the preimage.
Studdy Solution
Determine which option is correct:
- Based on the analysis, Option B is correct because a dilation centered at the origin leaves lines through the origin unchanged.
The correct statement is:
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