Georgia Department of Education
Georgia Standards of Excellence Framework
GSE Geometry • Unit 1
Culminating Task: Transforming Shapes
Name_________________________________
Date__________________
Draw a rectangle, parallelogram, square, or isosceles trapezoid in the coordinate plane so that
portions of the shape are in each of the four quadrants. Explain what would happen to your shape
if you transformed it using each of the given rules.
y
x
1. (–x, y)
2. (x, –y)
3. (x + 3, y)
4. (x, y – 2)
5. (x – 1, y + 4)
6. (2x, 2y)
7. (–x, –y)
8. (3x + 2, y – 1)
9. Which of the transformed figures are congruent to the original figure? Explain.
Mathematics  GSE Geometry  Unit 1: Transformations in the Coordinate Plane
July 2019  Page 85 of 87
Georgia Department of Education
Georgia Standards of Excellence Framework
GSE Geometry • Unit 1
10. Which of the transformed figures are NOT congruent to the original figure? Are any of these
figures similar? Explain.
11. If you make a new figure by adding 2 to the x– and y–coordinates of each side of your shape,
will the two figures be congruent, similar, or neither? Explain.
12. Create a rule or set of rules to make a 90 rotation of your figure. Explain how you decided
the rules for both x and y coordinates.
Point in Quadrant I:
(_________, _________) → (_________, _________)
Point in Quadrant II:
(_________, _________) → (_________, _________)
Point in Quadrant III:
(_________, _________) → (_________, _________)
Point in Quadrant IV:
(_________, _________) → (_________, _________)
In general:
(x, y)
→ (_________, _________)
13. Will a 90 rotation of any shape create congruent or similar figures? Explain.
14. What general conclusion can be made determining which transformations will produce
congruent figures in the plane?
Mathematics  GSE Geometry  Unit 1: Transformations in the Coordinate Plane
July 2019  Page 86 of 87
Georgia Department of Education
Georgia Standards of Excellence Framework
GSE Geometry • Unit 1
15. Describe a transformation (or a series of transformations) that will transform your figure onto
itself. Explain how you know this will transform your figure onto itself.
16. Describe a transformation that will make each side of the image parallel to the corresponding
side of the pre–image. Explain why this results in parallel lines.
17. Describe a transformation that will make each side of the image perpendicular to the
corresponding side of the pre–image. Explain why this results in parallel lines.
Mathematics  GSE Geometry  Unit 1: Transformations in the Coordinate Plane
July 2019  Page 87 of 87