Coordinates and moving shapes · Usually met around P4
Reflections
Same distance from the mirror, on the other side.
How to do it
Method
Same distance from the mirror, on the other side
Upright mirror through (4, 0): (1, 2) → (7, 2)
Another way
Fold the paper
Fold along the mirror: the image is where it lands
In full
A reflection is a mirror image: each point and its image are on opposite sides of the mirror line, the same distance from it. An upright mirror keeps the height (y) and flips across: 3 squares left of the line becomes 3 squares right. A mirror across keeps x and flips up and down. A 45° slanting mirror: measure along the squares' diagonals; when the line goes through (0, 0), (1, 1), (2, 2), …, the image of (x, y) is (y, x). When the mirror is one of the shape's sides, that side stays put and the shape flips over it. The size and shape stay the same; only the way it faces changes. Or imagine folding the paper along the mirror line: the image is where the shape lands.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The green line is a mirror line. Point A reflects to A′ at (□, □).
Fill in each box
Show the answer and working
Answer: 0，4
A is 4 squares from the mirror, so A′ is 4 on the other side, at the same height: (0, 4).
Example 2
The green line is a mirror line. Shape Q is the reflection of shape P.
True or false?
Show the answer and working
Answer: True
The reflection has each corner of P flipped to the other side of the mirror, the same distance from it.
Example 3
The mirror line slants through (0, 0), (1, 1), (2, 2), …. The point (1, 6) reflects to (□, □).
Fill in each box
Show the answer and working
Answer: 6，1
Measured along the squares' diagonals, the point and its image are the same distance from the line, and x and y swap: (6, 1).
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