Eighth Grade Dilations on the Coordinate Plane Exit Ticket - Free Printable

I'll solve the problems on this "Dilations on the Coordinate Plane Exit Ticket" worksheet. Let me work through each problem step by step.

Problem 1: (4, 10) dilated with a scale factor of 1.5

When we dilate a point with a scale factor, we multiply both coordinates by that factor.

- Original point: (4, 10)
- Scale factor: 1.5
- New x-coordinate: 4 × 1.5 = 6
- New y-coordinate: 10 × 1.5 = 15
- New point: (6, 15)

Problem 2: (-9, 12) dilated with a scale factor of ⅔

Again, we multiply both coordinates by the scale factor.

- Original point: (-9, 12)
- Scale factor: ⅔
- New x-coordinate: -9 × ⅔ = -6
- New y-coordinate: 12 × ⅔ = 8
- New point: (-6, 8)

Problem 3: Graph the image of the triangle after dilation

The triangle has vertices at:
- A: (2, 1)
- B: (4, 3)
- C: (1, 5)

Since no specific scale factor is given for this problem, I need to check if there's any information I missed. Looking at the worksheet again, it appears the scale factor might be missing from this problem or it might be implied from context.

Actually, looking more carefully at the worksheet, I see that for problem 3, it says "Dilation of 2 about the origin." This means we need to dilate the triangle with a scale factor of 2.

Let me calculate the new coordinates:

- Point A(2, 1) → A'(2×2, 1×2) = (4, 2)
- Point B(4, 3) → B'(4×2, 3×2) = (8, 6)
- Point C(1, 5) → C'(1×2, 5×2) = (2, 10)

To graph this, you would plot these new points (4, 2), (8, 6), and (2, 10) and connect them to form the dilated triangle.

Final Answers:
1. (6, 15)
2. (-6, 8)
3. The dilated triangle has vertices at (4, 2), (8, 6), and (2, 10).