SME
Grade 6 Math · Problem type
Reflect points across the axes
Use this for “Reflect (3, −4) across the x-axis. What are its new coordinates?”
Chart
(3, −2) reflected across the x-axis is (3, 2); across the y-axis (−3, −2); across both (−3, 2).
This is an example. Type your own values to start a new problem.
x-coordinate
example
y-coordinate
example
Opposite of the x-coordinate
calculated
Opposite of the y-coordinate
calculated
Quadrant
worked out (not typed)
Formulas
Quadrant of (3, −2): IV
Quadrant from the signs of the coordinates = quadrant
−3 = −3
The x-coordinate with its sign changed = opposite of the x-coordinate
−(−2) = 2
The y-coordinate with its sign changed = opposite of the y-coordinate
Assumptions
•
Across the x-axis the y-coordinate changes sign; across the y-axis the x-coordinate does.
•
Across both axes, both change sign.
•
Coordinates from −10,000 to 10,000. A point on an axis is in no quadrant.
Step-by-step
WE KNOW
x-coordinate: 3
y-coordinate: −2
FIND
quadrant, opposite of the x-coordinate, opposite of the y-coordinate
Step 1 · Find quadrant
Quadrant of (3, −2): ?
Quadrant from the signs of the coordinates = quadrant
Read the signs: (+, +) is I, (−, +) is II, (−, −) is III, (+, −) is IV.
3 > 0 and −2 < 0: (+, −)
Quadrant = IV
Step 2 · Find opposite of the x-coordinate
−3 = ?
The x-coordinate with its sign changed = opposite of the x-coordinate
Across the y-axis the point flips left to right: the x-coordinate changes sign.
Opposite of the x-coordinate = −3 (across the y-axis: (−3, −2))
Step 3 · Find opposite of the y-coordinate
−(−2) = ?
The y-coordinate with its sign changed = opposite of the y-coordinate
Across the x-axis the point flips top to bottom: the y-coordinate changes sign.
Opposite of the y-coordinate = 2 (across the x-axis: (3, 2); across both: (−3, 2))
Check
Put the numbers back in. Both sides should match.
Quadrant of (3, −2): IV ✓
−3 = −3 ✓
−(−2) = 2 ✓
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The coordinate plane: all four quadrants
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Polygons on the coordinate plane
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