Year 9 Maths • AC9M9SP02 • Authored homework
Similarity, enlargement and scale factors
Apply enlargement transformations to shapes and objects, using scale factors to identify similarity and calculate corresponding lengths, areas or model dimensions. Show working, use correct units or notation, and check reasonableness.
Part A
Short-answer questions
Define similar shapes.
What stays the same when a shape is enlarged?
What changes when a shape is enlarged by scale factor 3?
A side of length 4 cm is enlarged by scale factor 2.5. Find the new length.
A shape is reduced by scale factor 0.5. What happens to its side lengths?
Explain the difference between congruent and similar shapes.
Two corresponding sides are 6 cm and 15 cm. Find the scale factor from the smaller shape to the larger shape.
State why corresponding angles in similar shapes are equal.
Give one real-world use of scale factors.
Correct this misconception: “A scale factor always makes a shape bigger.”
Part B
Long-answer questions
A triangle has side lengths 3 cm, 4 cm and 5 cm. It is enlarged by scale factor 4. Find the new side lengths and compare the shapes.
Two rectangles are similar. The smaller is 5 cm by 8 cm and the larger has shortest side 20 cm. Find the longer side of the larger rectangle.
Explain how to test whether two triangles are similar using corresponding angles and side ratios.
A map scale is 1 cm represents 2 km. Find the real distance represented by 7.5 cm and explain the scale factor.
A model car is built at scale 1:24. The real car is 4.8 m long. Find the model length in centimetres.
Compare the effect of scale factor 3 on length and area using a simple square example.
A student doubles the sides of a rectangle and says the area also doubles. Explain the error with calculations.
Use coordinates to enlarge a simple triangle from the origin by scale factor 2 and list the new coordinates.
Create a scale drawing problem involving a room, map, model or diagram and solve it fully.
Write a full explanation of similarity, enlargement and scale factor using a labelled example.
Part C
Research and understanding task
Choose a real scale model, map, floor plan or enlarged image. Identify the scale factor, calculate at least two real or model dimensions, and explain what similarity means in that context.