A mirror on an axis
Show on a big screenStand a mirror along the y-axis. Where does the dot (5, 2) appear?
- P is (5, 2) and Q is (2, 6).
- The y-axis is the mirror. The images are (−5, 2) and (−2, 6).
- Both segments are 5 long.
The rule
It appears at (−5, 2).
Rule: In the y-axis, (x, y) goes to (−x, y). In the x-axis, (x, y) goes to (x, −y). Lengths stay the same. "In the y-axis" means the y-axis is the mirror. The mirrored dot is called the image.
Here x is the across number and y is the up number.
A mirror on the y-axis swaps left and right. So the across number changes sign. A mirror on the x-axis swaps up and down. So the up number changes sign.
The dot and its image are the same distance from the mirror. A dot on the mirror does not move. The dot (0, 4) is its own image in the y-axis.
| Mirror | P | Q | Across gap, up gap | Length |
|---|---|---|---|---|
| none | (5, 2) | (2, 6) | 3, 4 | √(9 + 16) = 5 |
| y-axis | (−5, 2) | (−2, 6) | 3, 4 | √(9 + 16) = 5 |
| x-axis | (5, −2) | (2, −6) | 3, 4 | √(9 + 16) = 5 |
The gaps are the same each time. So the length is the same each time.
Watch out!
Do not flip both signs. That turns the dot half way round the origin. It is not a mirror.
A mirror sits on an axis. Tap the image of the dot.
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Try the lab to finish this lesson.