To find the scale factor of the dilation, we need to compare corresponding lengths of the sides of the two parallelograms: $G'H'I'J'$ and $GHIJ$.

From the image:

1. Measure the length of one side of the original parallelogram $GHIJ$ (for example, $GH$).
2. Measure the length of the corresponding side in the dilated parallelogram $G'H'I'J'$ (such as $G'H'$).
3. The scale factor is the ratio of the length of a side of the dilated parallelogram to the corresponding side of the original parallelogram.

Let me measure and calculate these values for you. matplotlib.pyplot as plt import matplotlib.image as mpimg

Load and display the image

img_path = '/mnt/data/1739728120144b0fwnphd.jpg' img = mpimg.imread(img_path)

Display the image

plt.figure(figsize=(10, 10)) plt.imshow(img) plt.axis('on') plt.show()I can analyze the image and measure the relevant distances to calculate the scale factor.

Let's find the lengths of corresponding sides and compute the scale factor.

First, we need to determine the horizontal distance between points $G$ and $H$, and compare it with the distance between $G'$ and $H'$, as well as the vertical distance between corresponding points.

I will perform these calculations to determine the scale factor. Coordinates of the points from the image

G(-8, -10), H(-4, -2), G'(-4, -10), H'(-2, -2)

Calculate the distance between G and H (original)

from math import sqrt

Original coordinates (G and H)

G = (-8, -10) H = (-4, -2)

Distance GH

distance_GH = sqrt((H[0] - G[0])**2 + (H[1] - G[1])**2)

Coordinates of the dilated points (G' and H')

G_prime = (-4, -10) H_prime = (-2, -2)

Distance G'H'

distance_GH_prime = sqrt((H_prime[0] - G_prime[0])**2 + (H_prime[1] - G_prime[1])**2)

Calculate the scale factor

scale_factor = distance_GH_prime / distance_GH distance_GH, distance_GH_prime, scale_factorThe distance between points $G$ and $H$ (original parallelogram) is approximately 8.94 units, and the distance between points $G'$ and $H'$ (dilated parallelogram) is approximately 8.25 units.

The scale factor of the dilation is approximately $0.92$.

Would you like further details on the calculation or have other questions?

Here are some additional related questions to explore:

1. How do you calculate the dilation scale factor for other types of transformations like rotations or reflections?
2. What would happen if the scale factor was greater than 1 or less than 1?
3. How do you find the coordinates of dilated points using the scale factor?
4. How does the center of dilation affect the shape of the figure?
5. How can you determine the scale factor using graphing tools or software?

Tip: When calculating scale factors, it is important to use the same corresponding side measurements from both the original and dilated figures for accuracy.