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 reflect points across coordinate axes.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Coordinates and positive/negative positions.
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(−3,5) across the x-axis, then reflect its image across the y-axis. Find both images.
Why this math matters
A reflection places each point the same perpendicular distance on the opposite side of a mirror line. Identify the mirror line first, then compare perpendicular distances before using a coordinate rule.
Set up the model
A useful answer starts with clear assumptions:
- The mirror lines are exactly the coordinate axes.
- Apply the x-axis reflection first, then the y-axis reflection.
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.
Reflect points across coordinate axes
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Reflect P(−3,5) across the x-axis, then reflect its image across the y-axis. Find both images.
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
Across the x-axis: (x,y) → (x,−y)
The horizontal location stays fixed while the vertical displacement changes sign.
Apply the relationship
P′ = (−3,−5); across the y-axis: (x,y) → (−x,y)
The second reflection changes the horizontal sign of the already-reflected point.
Check and interpret
P″ = (3,−5)
Both coordinate signs have changed; this composition matches a half-turn about the origin.
The result
P″ = (3,−5)
Both coordinate signs have changed; this composition matches a half-turn about the origin.
Common mistakes to catch
- Reflecting across the x-axis changes y, not x.
- A single reflection reverses orientation, although it preserves distances.
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
Reflect (4,−2) across the y-axis.
Show a hint
Change the horizontal coordinate only.
Reveal answer and explanation
(−4,−2)
Equal perpendicular distances from the y-axis have opposite x signs.
Practice 2
Which points remain fixed when reflected across the x-axis?
Show a hint
Their perpendicular distance to the mirror must be zero.
Reveal answer and explanation
Every point with y = 0
Points already on the mirror line map to themselves.
Take the idea with you
Identify the mirror line first, then compare perpendicular distances before using a coordinate rule.
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: Rotate a point through a quarter-turn
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