Learn with Amar
Teaching video
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Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Scale a displacement from a specified dilation center.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Algebraic equations, ratios, angle and area facts, and basic coordinate geometry.
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 P=(5,4) by factor 2 about C=(1,1).
Why this math matters
State a transformation's center as well as its scale before mapping coordinates. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use Euclidean geometry and the angle, parallelism, similarity, or congruence conditions stated; a sketch alone does not establish them.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
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.
Dilate from a center other than the origin
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Dilate P=(5,4) by factor 2 about C=(1,1).
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 conditions
P−C=(4,3)
Find the displacement from the center, not from the origin.
Develop the calculation
2(P−C)=(8,6)
Scale that displacement in both coordinates.
Check and interpret
P′=C+2(P−C)=(9,7)
The center remains fixed and the center-to-point distance doubles.
The result
P′=C+2(P−C)=(9,7)
The center remains fixed and the center-to-point distance doubles.
Common mistakes to catch
- Multiplying coordinates directly works only for a dilation centered at the origin.
- A positive scale below one reduces distances from the center.
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
Where does C=(1,1) itself go under the same dilation?
Show a hint
Its displacement from the center is zero.
Reveal answer and explanation
(1,1)
Scaling zero and adding the center returns the same point.
Practice 2
Dilate (4,−2) by factor 1/2 about the origin.
Show a hint
Scale both coordinates directly because the center is zero.
Reveal answer and explanation
(2,−1)
The displacement is halved, producing a reduction.
Take the idea with you
State a transformation's center as well as its scale before mapping coordinates.
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: Derive a rotation from two intersecting reflections
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