What is the result of a dilation with a scale factor of 0.5?

What is the result of a dilation with a scale factor of 0.5?

• A. The figure becomes larger
• B. The figure remains the same size
• C. The figure shrinks by half
• D. The figure flips upside down

Answer: (C)

When a dilation is performed with a scale factor of 0.5, every point of the original figure is moved closer to the center of dilation by half the distance to that center. This effectively reduces the dimensions of the figure, resulting in a smaller size. In this case, since the scale factor is less than 1, it indicates a contraction. Specifically, the proportions of the figure remain the same, but all the sides are scaled down to half their original length, leading to a new figure that is half the size of the original in terms of area. Therefore, the correct interpretation of the result is that the figure shrinks by half, making it a smaller version of the original shape while maintaining its shape and proportions.

When a dilation is performed with a scale factor of 0.5, every point of the original figure is moved closer to the center of dilation by half the distance to that center. This effectively reduces the dimensions of the figure, resulting in a smaller size.

In this case, since the scale factor is less than 1, it indicates a contraction. Specifically, the proportions of the figure remain the same, but all the sides are scaled down to half their original length, leading to a new figure that is half the size of the original in terms of area. Therefore, the correct interpretation of the result is that the figure shrinks by half, making it a smaller version of the original shape while maintaining its shape and proportions.