Question

given that the area of the preimage is 4, and the area of the image 1, what is the ratio of the areas? * 4 points your answer

Explanation:

Step1: Identify preimage and image areas

Preimage area = 4, Image area = 1.

Step2: Calculate area ratio

Ratio = Preimage area / Image area = \( \frac{4}{1} = 4:1 \) (or \( \frac{1}{4} \) if image:preimage, but problem says "ratio of the areas" likely preimage to image). Wait, ratio of preimage to image area: 4 to 1, or image to preimage 1 to 4. Wait, the question says "the ratio of the areas" – usually, ratio of preimage (original) to image (transformed) or vice versa? Let's check: preimage area 4, image 1. So ratio of preimage area to image area is 4:1, or image to preimage is 1:4. But let's see the problem statement: "the ratio of the areas" – probably preimage (black triangle) to image (red triangle). So 4:1, or as a fraction 4/1 = 4, or 1/4 if image to preimage. Wait, let's re-read: "Given that the area of the preimage is 4, and the area of the image 1, what is the ratio of the areas?" So ratio of preimage area to image area is 4:1, or 4/1 = 4. Or maybe image to preimage? Wait, the problem says "the ratio of the areas" – maybe preimage to image, so 4:1, or 4/1 = 4. Wait, but let's confirm: ratio of areas is preimage area divided by image area, so 4/1 = 4, or 4:1.

Answer:

4:1 (or \( \frac{4}{1} \), or 4)