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Teaching video
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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to connect dilation with length and area factors.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Coordinate scaling and triangle area.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Dilate triangle O(0,0), A(4,0), B(0,6) about the origin by factor 1/2. Find its vertices and compare the two areas.
Why this math matters
An origin-centred dilation multiplies coordinates by a scale factor; lengths scale by that factor and areas by its square. Check whether an enlargement changes one, two, or three dimensions before choosing a power of its scale factor.
Set up the model
A useful answer starts with clear assumptions:
- The dilation centre is the origin.
- The scale factor is positive and applies uniformly in both directions.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Connect dilation with length and area factors
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Dilate triangle O(0,0), A(4,0), B(0,6) about the origin by factor 1/2. Find its vertices and compare the two areas.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
(x,y) → (x/2,y/2); O′(0,0), A′(2,0), B′(0,3)
Each coordinate and each leg length is halved.
Apply the relationship
original area = (1/2)(4)(6) = 12; image area = (1/2)(2)(3) = 3
Both base and height change, so the area changes twice multiplicatively.
Check and interpret
length factor = 1/2; area factor = 3/12 = 1/4
The image is similar to the original, with area multiplied by (1/2)².
The result
length factor = 1/2; area factor = 3/12 = 1/4
The image is similar to the original, with area multiplied by (1/2)².
Common mistakes to catch
- Area and length do not use the same scale factor.
- Adding the same amount to each coordinate is a translation, not a dilation.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A dilation by factor 3 changes a 5 cm segment to what length?
Show a hint
Lengths use the scale factor once.
Reveal answer and explanation
15 cm
3 × 5 = 15.
Practice 2
A similar figure has area 9 times the original. What is its positive length scale factor?
Show a hint
Find the positive square root of the area factor.
Reveal answer and explanation
3
k² = 9 with k > 0 gives k = 3.
Take the idea with you
Check whether an enlargement changes one, two, or three dimensions before choosing a power of its scale factor.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Establish congruence with a sequence of motions
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