Question

preimage
image
what is the length of side hi in the preimage?
92
46
23
70

Explanation:

Step1: Identify the scale factor

First, we find the scale factor by comparing the corresponding sides. The side GH in the preimage is 32, and the corresponding side in the image (let's say the vertical side, maybe GH or similar) is 80. Wait, actually, looking at the preimage and image, the preimage has a side GH of length 32, and the image has a side (maybe the vertical one) of length 80. Wait, no, maybe the horizontal sides? Wait, the preimage has a side (let's see, the preimage is a quadrilateral, and the image is a parallelogram. Wait, maybe the vertical side in preimage is 32, and in image is 80. So the scale factor \( k \) is \( \frac{80}{32} = 2.5 \).

Step2: Find the length of HI in preimage

The length of HI in the image is 115. Since the image is a scaled version of the preimage, the length of HI in the preimage \( x \) satisfies \( x \times k = 115 \). We know \( k = 2.5 \), so \( x = \frac{115}{2.5} \).

Calculating \( \frac{115}{2.5} \): multiply numerator and denominator by 2 to eliminate the decimal, we get \( \frac{230}{5} = 46 \).

Answer:

46 (corresponding to the option "46")