Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Track a point through two reflections in parallel lines.
- 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
Reflect P=(1,2) across x=0, then across x=3. Find the final point.
Why this math matters
Analyze a complicated motion by applying its simple transformations one at a time. 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.
Two parallel reflections create a translation
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Reflect P=(1,2) across x=0, then across x=3. Find the final point.
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
Across x=0: (1,2)→(−1,2)
Reflect the horizontal coordinate while preserving y.
Develop the calculation
Across x=3: x′=2(3)−(−1)=7
The new point lies the same four-unit distance on the other side of x=3.
Check and interpret
Final point (7,2): translation by (6,0)
The displacement is twice the three-unit separation of the reflection lines.
The result
Final point (7,2): translation by (6,0)
The displacement is twice the three-unit separation of the reflection lines.
Common mistakes to catch
- Composition order affects the resulting displacement.
- A reflection changes orientation, while two reflections together preserve orientation.
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
Reverse the order of those two reflections on (1,2).
Show a hint
Reflect across x=3 first, then x=0.
Reveal answer and explanation
(−5,2)
The point moves to (5,2) then (−5,2), a six-unit translation left.
Practice 2
Do reflections preserve a figure's area?
Show a hint
They are rigid motions.
Reveal answer and explanation
Yes
Each reflection preserves lengths and angles, so it preserves area as well.
Take the idea with you
Analyze a complicated motion by applying its simple transformations one at a time.
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: Find the possible lengths of a third side
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