Question

1. a 20 b, 68, 64, d 24 c; e d, b a; dilation factor \\(\frac{1}{2}\\)

Explanation:

Step1: Identify original and dilated lengths

Original length (e.g., AB = 20, BC = 64? Wait, maybe AB = 20, DC = 24? Wait, the first rectangle has AB = 20, DC = 24, and height (AD or BC) – AD is 68, BC is 64? Wait, maybe it's a rectangle, so opposite sides should be equal. Maybe a typo, but the dilation factor is 1/2. Let's take a side, say AB = 20. After dilation, the corresponding side (A'B') should be 20 1/2 = 10? Wait, or maybe the height. Wait, the second rectangle's height is 64? Wait, no, the dilation factor is 1/2. Let's check a side. Suppose original length is 24 (DC), then dilated length would be 24 1/2 = 12. Or AB = 20, dilated to 10. Or height: if original height is 64 (BC), then dilated height is 64 1/2 = 32? Wait, maybe the problem is to verify the dilation factor. Let's take AB = 20, then A'B' should be 20 1/2 = 10. Or DC = 24, so D'C' = 24 1/2 = 12. Or AD = 68, then A'D' = 68 1/2 = 34? Wait, maybe the figure has some errors, but the dilation factor is 1/2. So to find a dilated length, multiply original by 1/2.

Step2: Let's take AB = 20. Dilated length A'B' = 20 (1/2) = 10. Or DC = 24, D'C' = 24 (1/2) = 12. Or BC = 64, B'C' = 64 (1/2) = 32. Or AD = 68, A'D' = 68 (1/2) = 34.

Answer:

If we take AB = 20, dilated length is 10; DC = 24, dilated is 12; BC = 64, dilated is 32; AD = 68, dilated is 34. (Depending on the corresponding side, but the dilation factor is 1/2, so multiply original length by 1/2.)