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 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to translate a figure with one shared movement.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Coordinate plotting and signed addition.
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
Translate triangle A(1,2), B(4,2), C(1,5) three units left and two units up. Find its image vertices.
Why this math matters
A translation adds the same horizontal and vertical changes to every point, preserving shape, size, and orientation. Use a translation rule to relocate an entire drawing while preserving its dimensions.
Set up the model
A useful answer starts with clear assumptions:
- The axes have their standard orientation.
- Exactly the same movement is applied to every vertex.
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.
Translate a figure with one shared movement
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Translate triangle A(1,2), B(4,2), C(1,5) three units left and two units up. Find its image vertices.
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
translation rule: (x,y) → (x − 3, y + 2)
Left decreases the horizontal coordinate; up increases the vertical coordinate.
Apply the relationship
A′(−2,4), B′(1,4), C′(−2,7)
Apply both coordinate changes to each original point.
Check and interpret
A′B′ = 3 and A′C′ = 3, matching AB and AC
A common movement preserves the original side lengths and the triangle's orientation.
The result
A′B′ = 3 and A′C′ = 3, matching AB and AC
A common movement preserves the original side lengths and the triangle's orientation.
Common mistakes to catch
- A translation never changes only selected vertices.
- Do not interchange the horizontal and vertical changes.
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
Under (x,y) → (x + 5,y − 1), where does (−4,3) go?
Show a hint
Add each specified change to its coordinate.
Reveal answer and explanation
(1,2)
−4 + 5 = 1 and 3 − 1 = 2.
Practice 2
What translation maps (2,−1) to (−3,4)?
Show a hint
Compute final minus initial for each coordinate.
Reveal answer and explanation
Five left and five up
The change is (−3 − 2, 4 − (−1)) = (−5,5).
Take the idea with you
Use a translation rule to relocate an entire drawing while preserving its dimensions.
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: Reflect points across coordinate axes
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