Reflections in lines
Objective. Reflect shapes in axes and lines parallel to the axes.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Reflection in a line creates a mirror image where every point and its image are equidistant from the mirror line, on perpendicular lines through it. For reflections in the axes, flip the sign of the coordinate perpendicular to that axis: reflecting in the x-axis sends (x, y) to (x, −y), and in the y-axis sends (x, y) to (−x, y). For lines like x = 3 or y = −1, measure the distance from each point to the line and place the image the same distance on the other side. Example: reflecting (2, 5) in the line y = 1 gives (2, −3), since 5 is 4 above the line so the image is 4 below it.
Worked example
Reflect the point (1, 4) in the line y = 2, giving the coordinates of the image.
- 1The mirror line is horizontal: y = 2, so only the y-coordinate changes.
- 2Distance from y = 4 to the line y = 2 is 2 units.
- 3Place the image 2 units on the other side of the line: y = 2 − 2 = 0.
- 4The x-coordinate stays the same, so the image is (1, 0).
Answer: (1, 0)
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Practice
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Start practisingCommon mistake. Pupils often reflect (2, 5) in x = 3 by swapping coordinates to (5, 2) instead of measuring horizontal distance; correct image is (4, 5), since 2 is 1 left of x = 3, so the image is 1 right of it.
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