Reflection in Coordinate Geometry explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Reflection means flipping a point or shape across a line.
In coordinate geometry, we can find the reflected image by changing coordinates in a clear way.
Reflection is used in graphs, symmetry, transformations, design, and computer graphics.
A reflection creates a mirror image.
The line used as the mirror is called the line of reflection.
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When a point is reflected, its distance from the mirror line stays the same.
The point and its image lie on opposite sides of the mirror line, unless the point is already on the line.
Coordinate rules help us reflect points quickly without drawing every distance.
Meaning: A reflection flips a point or shape across a line.
Definition: The original point and reflected point are the same distance from the line of reflection.
If a point is 3 units above the xis, its reflection is 3 units below the xis.
Meaning: The xis acts like a mirror.
Definition: (x, y) becomes (x, -y).
The oordinate stays the same. The oordinate changes sign.
Meaning: The xis acts like a mirror.
Definition: (x, y) becomes (-x, y).
The oordinate stays the same. The oordinate changes sign.
Meaning: A point on the mirror line does not move.
Definition: If a point lies on the line of reflection, its image is the same point.
A point on the xis has , so changing the sign of y makes no difference.
Easy
Question: Reflect A(4, 3) in the xis.
Medium
Question: Reflect B(-5, 2) in the xis.
Exam-level
Question: A point P(a, -6) is reflected in the xis to P'(3, -6). Find a.
Changing both coordinates for xis reflection
Why it happens: The rule is memorised without meaning.
Correct approach: For xis reflection, change only the oordinate sign.
Changing y for xis reflection
Why it happens: Axis names are confused.
Correct approach: For xis reflection, change only the oordinate sign.
Forgetting negative signs
Why it happens: The reflected point is not checked on the grid.
Correct approach: Plot the point mentally to check the side of the axis.
Does reflection change the size of a shape?
No. It only flips the shape.
What happens to a point on the xis when reflected in the xis?
It stays in the same place.
How can I check my reflected point?
Check that it is the same distance from the mirror line on the opposite side.
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