Let’s solve each dilation problem step by step. Remember: when you dilate a shape using center (0, 0), you multiply every coordinate of the shape’s points by the scale factor.
---
Problem 1: Dilate by 2 using center (0, 0)
We have a line segment with endpoints at approximately (-3, 0) and (4, 1).
Multiply each coordinate by 2:
- (-3, 0) → (-6, 0)
- (4, 1) → (8, 2)
Draw a new line from (-6, 0) to (8, 2).
---
Problem 2: Dilate by 1/4 using center (0, 0)
The triangle has vertices at approximately:
A = (-5, -2), B = (7, 5), C = (6, -5)
Multiply each coordinate by 1/4:
- A: (-5 × 1/4, -2 × 1/4) = (-1.25, -0.5)
- B: (7 × 1/4, 5 × 1/4) = (1.75, 1.25)
- C: (6 × 1/4, -5 × 1/4) = (1.5, -1.25)
Plot these three new points and connect them to form the smaller triangle.
---
Problem 3: Dilate by 1/4 using center (0, 0)
Triangle vertices:
A = (-4, 2), B = (0, 4), C = (4, 2)
Multiply each by 1/4:
- A: (-4 × 1/4, 2 × 1/4) = (-1, 0.5)
- B: (0 × 1/4, 4 × 1/4) = (0, 1)
- C: (4 × 1/4, 2 × 1/4) = (1, 0.5)
Connect these points — it will be a small triangle centered near the origin.
---
Problem 4: Dilate by 2 using center (0, 0)
Quadrilateral vertices (approximate):
A = (-1, -2), B = (1, -3), C = (2, 0), D = (0, 3)
Multiply each by 2:
- A: (-2, -4)
- B: (2, -6)
- C: (4, 0)
- D: (0, 6)
Plot these four points and connect them in order to get the enlarged shape.
---
Final Answer:
For each graph, redraw the shape using the new coordinates calculated by multiplying original coordinates by the given scale factor (2 or 1/4), keeping (0, 0) as the center. The resulting shapes are the dilated images.
Parent Tip: Review the logic above to help your child master the concept of dilation worksheet.
