https://file.aiquickdraw.com/mathbot/file/1725482438727pgxnbmaf.jpg

To solve the problem of finding the weighted average of the points shown in the image:

### Given:
- Point \( x \) has a weight of 3.
- Point \( y \) has a weight of 1.

In the weighted average formula for two points, the coordinates of the weighted average point \( r \) are found using the following formula:

\[
r_x = \frac{w_1 \cdot x_1 + w_2 \cdot y_1}{w_1 + w_2}
\]
\[
r_y = \frac{w_1 \cdot x_2 + w_2 \cdot y_2}{w_1 + w_2}
\]

Where:
- \( w_1 \) and \( w_2 \) are the weights of points \( x \) and \( y \), respectively.
- \( x_1 \), \( x_2 \) are the coordinates of point \( x \).
- \( y_1 \), \( y_2 \) are the coordinates of point \( y \).

### Approach:
1. Extract the coordinates of points \( x \) and \( y \) from the graph.
2. Apply the weighted average formula to calculate the coordinates of point \( r \).

Let me take a closer look at the graph to extract the coordinates and calculate the weighted average.

from PIL import Image

# Load the uploaded image to take a closer look at the coordinates
image_path = '/mnt/data/1725482438727pgxnbmaf.jpg'

# Open the image
img = Image.open(image_path)
img.show()The image is now open for closer inspection. 

To proceed with calculating the weighted average, let's first identify the coordinates of points \( x \) and \( y \) based on the visual information from the graph. Once we have those coordinates, we can apply the formula to compute the weighted average.

Please provide the coordinates of points \( x \) and \( y \), or I can estimate them based on the image.

Find the coordinates of r that represent the weighted average for the given set of points with the given weights: x has a weight of 3, y has a weight of 1.

Learn how to find the coordinates of a point that represents the weighted average of two points with given weights. This example demonstrates the application of the weighted average formula in coordinate geometry, suitable for students in Grades 7-9.

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