Use Four Quadrants and Coordinate Reflections

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: Reflect (−5,3) across the y-axis to get (5,3).
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Signed coordinates locate points on both sides of each axis. Changing an x sign reflects across the y-axis; changing a y sign reflects across the x-axis. Points sharing one coordinate have an axis-aligned distance found from the other coordinates. Across zero, that distance includes both sides.

Read both coordinate signs and plot relative to the origin. Apply the requested reflection by changing only the perpendicular coordinate’s sign. Check that the distance to the reflecting axis is unchanged and the other coordinate stays fixed.

Name the reflecting axis before changing a sign. A y-axis reflection changes x, not y. Draw both axes through zero and label all four sign combinations.

1. Draw both axes through zero and label all four sign combinations.
2. Work through the supplied example and label what each number or attribute represents.
3. Read both coordinate signs and plot relative to the origin.
4. Answer the check, then try the three changed-input practice questions and explain one correction.

Check your reasoning

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Take it further

Points (−3,4) and (5,4) are eight units apart; reflecting (2,−6) across x gives (2,6).

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