I will solve this worksheet by analyzing each of the 9 graphs to determine the type of geometric transformation shown. The main types of transformations are translation, reflection, rotation, and dilation.
Let me start by examining each graph one by one.
Graph 1
- Original triangle ABC is in the third quadrant.
- Transformed triangle A'B'C' is in the first quadrant.
- Point A(-4,-3) moves to A'(2,0), B(-3,-1) moves to B'(3,3), C(-1,-2) moves to C'(4,1).
- All points have moved 6 units right and 3 units up.
- This is a
translation.
Graph 2
- Original points M(0,0), N(2,1), O(3,0) become M'(0,0), N'(3,2), O'(4,0).
- M stays at the same point, while others move.
- The shape appears to be stretched away from point M.
- This looks like a
dilation centered at M.
Graph 3
- Points P(-4,-2), Q(-2,0) become P'(4,2), Q'(2,0).
- Each point (x,y) becomes (-x,-y), which is a 180° rotation about the origin.
- This is a
rotation.
Graph 4
- Original quadrilateral ABCD is above the x-axis, transformed A'B'C'D' is below.
- Points appear to be reflected across the x-axis.
- For example, if A is at (-5,2), A' is at (-5,-2).
- This is a
reflection across the x-axis.
Graph 5
- Points D(-3,1), E(-1,3) become D'(3,1), E'(1,3).
- The x-coordinates change sign, y-coordinates remain the same.
- This is a
reflection across the y-axis.
Graph 6
- Points K(3,4), L(3,-2) become K'(1,2), L'(1,-1).
- J(0,0) remains at J'(0,0).
- The figure is scaled down toward point J.
- This is a
dilation centered at J.
Graph 7
- Original triangle ABC and transformed A'B'C' appear to be rotated around the origin.
- Point A(-4,-4) becomes A'(-4,4), which suggests a 90° counterclockwise rotation or reflection across the x-axis.
- Looking at multiple points: A(-4,-4) → A'(-4,4), B(-2,-2) → B'(-2,2), C(-1,-1) → C'(-1,1).
- All y-coordinates change sign, so this is a
reflection across the x-axis.
Graph 8
- Original trapezoid GHJI and transformed G'H'J'I' are on opposite sides of the y-axis.
- Points G(-2,3) → G'(2,3), H(-1,3) → H'(1,3), I(-3,0) → I'(3,0), J(0,0) → J'(0,0).
- X-coordinates change sign, y-coordinates stay the same.
- This is a
reflection across the y-axis.
Graph 9
- Points M(-3,3), P(-3,-3) become M'(3,3), P'(3,-3).
- The figure is reflected across the y-axis.
- Also, N(0,0) remains at N'(0,0).
- This is a
reflection across the y-axis.
Now I'll summarize my findings for each graph:
1. Translation
2. Dilation
3. Rotation
4. Reflection (across x-axis)
5. Reflection (across y-axis)
6. Dilation
7. Reflection (across x-axis)
8. Reflection (across y-axis)
9. Reflection (across y-axis)
This completes the analysis of all 9 transformations on the worksheet.
Parent Tip: Review the logic above to help your child master the concept of identify transformations worksheet.
