Enlargement is a transformation that resizes a shape by a scale factor from a fixed centre point — a scale factor greater than 1 makes it bigger, between 0 and 1 makes it smaller, keeping the shape's angles and proportions identical (similar) while its size changes. Designing an algorithm for a geometric construction means breaking a construction (like bisecting an angle, or constructing a perpendicular line) into a precise, ordered sequence of steps and decisions — similar to a recipe — that produces a reliable, repeatable result every time it's followed, regardless of who follows it.
Example
Enlarging a triangle with vertices (1,1), (2,1), (1,3) by a scale factor of 3 from the origin multiplies every coordinate by 3, giving (3,3), (6,3), (3,9) — a triangle three times the size, in exactly the same proportions, just further from the origin. An algorithm for constructing an equilateral triangle might specify: draw a line segment, then from each endpoint draw an arc with the same radius as the segment, and connect the intersection point to both endpoints.
Key terms
Enlargement:
A transformation that resizes a shape by a scale factor from a fixed centre point.
Algorithm:
A precise, ordered sequence of steps that reliably produces the same result.
Questions
1. Enlargement is a transformation that:
Resizes a shape by a scale factor
Only rotates a shape
Only reflects a shape
Removes a shape entirely
2. A scale factor greater than 1 makes a shape:
Bigger
Smaller
Identical in size
Disappear
3. A scale factor between 0 and 1 makes a shape:
Smaller
Bigger
Rotate only
Reflect only
4. An enlarged shape keeps its:
Angles and proportions (it stays similar)
Exact original size
Nothing in common with the original
Only its colour
5. An algorithm is:
A precise, ordered sequence of steps
A random guess
A single unrelated fact
A type of shape
6. A geometric construction algorithm should produce:
A reliable, repeatable result every time
A different result every time
No result at all
Only a rough estimate
7. Enlarging point (2, 3) by a scale factor of 2 from the origin gives:
(4, 6)
(2, 3)
(1, 1.5)
(4, 3)
8. Enlarge point (1, 4) by a scale factor of 3 from the origin:
(3, 12)
(1, 4)
(4, 12)
(3, 4)
9. A shape enlarged by a scale factor of 0.5 will:
Be half the size of the original
Be double the size of the original
Stay exactly the same size
Disappear completely
10. Two shapes are "similar" when they have:
The same angles and proportional sides, but possibly different sizes
Identical sizes and identical angles only
No relationship to each other
Different angles but the same size
11. Why must every step in a geometric construction algorithm be precisely defined, rather than left to interpretation?
Vague steps could be followed differently by different people, producing inconsistent results
Precision in an algorithm never affects its reliability
Geometric constructions never need any precise steps
Any interpretation of a step always produces an identical result
12. A triangle with sides 3, 4, 5 is enlarged by a scale factor of 4. What are the new side lengths?
12, 16, 20
7, 8, 9
3, 4, 5
9, 12, 15
13. Why does a scale factor of exactly 1 leave a shape completely unchanged?
Multiplying every coordinate by 1 doesn't change its value
A scale factor of 1 always doubles a shape
A scale factor of 1 is not actually a valid transformation
Scale factor has no connection to how a shape changes
14. A map uses a scale of 1:50,000. A road measuring 4cm on the map represents what real distance?
2km
200m
20km
0.2km
15. Why might dynamic geometry software be useful for testing and refining a geometric construction algorithm before finalising it?
It allows quickly checking whether the algorithm produces a correct, consistent result across many different starting conditions
Software can never be used to test geometric constructions
Testing an algorithm never reveals whether it actually works correctly
Geometric algorithms never need any testing or refinement
16. Why is enlargement considered different from other transformations like rotation or reflection, in terms of what changes and what stays the same?
Enlargement changes a shape's size while preserving its angles and proportions, while rotation and reflection preserve size but change orientation or position
All transformations change both size and shape identically
Enlargement changes a shape's angles but keeps its exact size
There is no meaningful difference between these types of transformations
17. Why might an architect use enlargement principles when creating a scale model of a building?
A consistent scale factor lets every dimension of the model accurately and proportionally represent the real building
Scale models never actually use any mathematical scale factor
Enlargement principles have no practical application in architecture
A scale model could use a different scale factor for each dimension with no issue
18. Why might designing an algorithm for a geometric construction be considered good preparation for computer programming, even though no computer is involved?
Both require breaking a problem into a precise, logical, ordered sequence of steps that produces a reliable outcome
Geometric construction and programming have no meaningful connection to each other
Algorithms are a concept unique to computer programming with no other application
Precision and ordering of steps matter in programming but not in geometric construction
19. A model train is built at a scale of 1:87. If a real train carriage is 17.4m long, how long is the model, and why does this calculation rely on the same principle as enlargement?
Approximately 20cm — dividing by the scale factor uses the same proportional relationship that enlargement uses to resize a shape
Approximately 2m — scale models are never mathematically related to enlargement
Approximately 87cm — the scale factor is simply added to the original length
The model's length cannot be calculated from the scale alone
20. Why might two different algorithms, both correctly constructing an equilateral triangle, look different in their steps but still be equally valid?
Multiple valid step-by-step sequences can achieve the same correct geometric result, as long as each is logically precise and reliable
Only one single possible algorithm can ever exist for any given geometric construction
If two algorithms have different steps, at least one of them must be producing an incorrect result
Geometric algorithms can never be validly written in more than one way
21. Understanding enlargement, similarity and geometric algorithms mainly helps you to:
Analyse how shapes change under scaling, and design reliable step-by-step geometric processes
Assume enlarging a shape always changes its angles
Avoid ever using precise, ordered steps for geometric constructions
Treat similar and identical shapes as meaning exactly the same thing
Answer key (parent copy)
1. Resizes a shape by a scale factor
2. Bigger
3. Smaller
4. Angles and proportions (it stays similar)
5. A precise, ordered sequence of steps
6. A reliable, repeatable result every time
7. (4, 6)
8. (3, 12)
9. Be half the size of the original
10. The same angles and proportional sides, but possibly different sizes
11. Vague steps could be followed differently by different people, producing inconsistent results
12. 12, 16, 20
13. Multiplying every coordinate by 1 doesn't change its value
14. 2km
15. It allows quickly checking whether the algorithm produces a correct, consistent result across many different starting conditions
16. Enlargement changes a shape's size while preserving its angles and proportions, while rotation and reflection preserve size but change orientation or position
17. A consistent scale factor lets every dimension of the model accurately and proportionally represent the real building
18. Both require breaking a problem into a precise, logical, ordered sequence of steps that produces a reliable outcome
19. Approximately 20cm — dividing by the scale factor uses the same proportional relationship that enlargement uses to resize a shape
20. Multiple valid step-by-step sequences can achieve the same correct geometric result, as long as each is logically precise and reliable
21. Analyse how shapes change under scaling, and design reliable step-by-step geometric processes