Giving
P(-2, -3)
Q(-1, -3)
R(-3, -3)

and (x, y) -> (2x + 4, y)
Find the new coordinates

Given the transformation \((x, y) \to (2x + 4, y)\) and the initial coordinates of points \(P\), \(Q\), and \(R\):

- **Point P**: \((-2, -3)\)
- **Point Q**: \((-1, -3)\)
- **Point R**: \((-3, -3)\)

### Applying the Transformation

To find the new coordinates, apply the transformation rule to each point:

1. **For Point P** \((-2, -3)\):

\[
x' = 2(-2) + 4 = -4 + 4 = 0, \quad y' = -3
\]

New coordinates of \(P'\) are \((0, -3)\).

2. **For Point Q** \((-1, -3)\):

\[
x' = 2(-1) + 4 = -2 + 4 = 2, \quad y' = -3
\]

New coordinates of \(Q'\) are \((2, -3)\).

3. **For Point R** \((-3, -3)\):

\[
x' = 2(-3) + 4 = -6 + 4 = -2, \quad y' = -3
\]

New coordinates of \(R'\) are \((-2, -3)\).

### New Coordinates after Transformation

- \(P' = (0, -3)\)
- \(Q' = (2, -3)\)
- \(R' = (-2, -3)\)

### Summary

The points after the transformation are:
- \(P' = (0, -3)\)
- \(Q' = (2, -3)\)
- \(R' = (-2, -3)\)

### Do you need more details or have any questions?

Here are some follow-up questions to consider:

1. What is the distance between the transformed points \(P'\), \(Q'\), and \(R'\)?
2. How does the transformation affect the alignment of the points?
3. Would the transformation \((x, y) \to (2x, 2y)\) result in a similar or different set of points?
4. What type of transformation keeps both coordinates of each point unchanged?
5. How would you graphically represent the original and transformed points on the coordinate plane?

**Tip:** Transformations can alter the positioning of points on a graph, leading to changes in shape, size, or orientation. Understanding how each transformation affects the points can help in visualizing geometric changes.

Explore how to apply the transformation (x, y) -> (2x + 4, y) to coordinates (-2, -3), (-1, -3), and (-3, -3). Learn the new coordinates of each point after transformation. Suitable for Grades 9-12 students studying coordinate geometry.

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