Suppose you copy a drawing of a polygon with the given size factor. How will the side lengths, angle measures, and perimeter of the image compare to those of the original?
A.) 200%
B.) 150%
C.) 50%
D.) 75%
To compare the side lengths, angle measures, and perimeter of the image to those of the original, you need to understand the concept of scaling or similar figures.
When you copy a drawing of a polygon with a specific size factor, all the side lengths of the image will be multiplied by that factor. Similarly, all the angle measures will remain the same.
Therefore, the side lengths, angle measures, and perimeter of the image will relate directly to the size factor. If the size factor is greater than 100%, it means the image is enlarged; if it is less than 100%, the image is reduced.
Let's consider the answer choices:
A.) 200%: This means that the image is enlarged to twice the size of the original. Therefore, the side lengths of the image will be doubled, angle measures will remain the same, and the perimeter will be doubled.
B.) 150%: This means that the image is enlarged to 1.5 times the size of the original. Therefore, the side lengths of the image will be multiplied by 1.5, angle measures will remain the same, and the perimeter will be multiplied by 1.5.
C.) 50%: This means that the image is reduced to half the size of the original. Therefore, the side lengths of the image will be halved, angle measures will remain the same, and the perimeter will be halved.
D.) 75%: This means that the image is reduced to 0.75 times the size of the original. Therefore, the side lengths of the image will be multiplied by 0.75, angle measures will remain the same, and the perimeter will be multiplied by 0.75.
Based on the explanations above, the correct answer is C.) 50%, as it correctly states that the side lengths of the image will be halved, angle measures will remain the same, and the perimeter will be halved compared to the original polygon.