https://file.aiquickdraw.com/mathbot/file/1728983122274frg95z7w.jpg

In this problem, you're asked to reflect the triangle \(\triangle PQR\) over the y-axis. To perform a reflection over the y-axis, you reverse the sign of the x-coordinates of each vertex, while keeping the y-coordinates unchanged.

Here are the current coordinates of the triangle's vertices:
- \(P(-8, 2)\)
- \(Q(-4, -2)\)
- \(R(-6, -4)\)

Now, let's reflect them over the y-axis:
- The reflection of \(P(-8, 2)\) is \(P'(8, 2)\).
- The reflection of \(Q(-4, -2)\) is \(Q'(4, -2)\).
- The reflection of \(R(-6, -4)\) is \(R'(6, -4)\).

Now, plot the reflected points \(P'(8, 2)\), \(Q'(4, -2)\), and \(R'(6, -4)\) on the graph. Connect the points to form the new triangle \(\triangle P'Q'R'\).

Would you like more details or have any questions?

Here are five related questions to explore:
1. What changes occur when reflecting a shape over the x-axis instead?
2. How do you find the reflection of a point over the origin?
3. What are the rules for reflecting over lines other than the x- or y-axis (e.g., \(y = x\))?
4. What happens to the area of a triangle when it is reflected?
5. How can you verify the accuracy of your reflection?

**Tip:** When reflecting across an axis, remember that the axis acts like a "mirror," so the distance from the point to the axis should be preserved, but the direction changes.

Graph the image of ∆PQR after a reflection over the y-axis.

This problem demonstrates how to reflect a triangle ∆PQR across the y-axis. Learn to apply coordinate transformations to find the new points: P(-8, 2) → P'(8, 2), Q(-4, -2) → Q'(4, -2), and R(-6, -4) → R'(6, -4). The solution explores essential concepts in reflections and transformations, suitable for Grade 8 students.

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