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Step 1:I'll solve this step by step using the provided guidelines:
Step 2:: Understand Dilation
A dilation is a transformation that changes the size of a figure while keeping its shape similar. It involves: - A center point of dilation - A scale factor (how much the figure is enlarged or reduced) - Preserving the original shape's proportions
Step 3:: Analyze the Graphs
Let's examine each graph for characteristics of dilation: - Graph A: Appears to be a rotation - Graph B: Looks like a translation (slide) - Graph C: Shows a clear change in size while maintaining shape proportions
Step 4:: Confirm Dilation Characteristics
In the graph of C: - The original figure is scaled up - All points move away from or toward a single center point - The shape remains proportionally identical to the original
Step 5:: Verify Scale Factor
The figure in graph C demonstrates: - Consistent enlargement of all points - Proportional increase in distances from a center point
Final Answer
The key distinguishing feature is that graph C maintains the original shape's proportions while changing its size, which is the defining characteristic of a dilation.
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