Every negative number has a positive twin. Every fraction has a flipped partner. Fold the number line at the right spot and one value becomes another. Today you explore four kinds of mathematical mirrors.
Read your shirt in the mirror: the letters flip left to right, that is a reflection. Numbers and shapes flip the exact same way.
Fold a strip of paper at zero and every point lands on top of another point, the same distance away, on the opposite side. That is a reflection. You can fold at zero, or fold anywhere you like, at a mirror line.
Slide the point x and the mirror line m. The image lands exactly as far past the mirror as x started from it.
Slide x and watch two segments grow from 0, one to x, one to its opposite. They are always the same length, because distance does not care which direction you go.
A number and its opposite sit the same distance from 0, on either side. Added together, they always land back on 0.
The reciprocal keeps the same sign but flips the size: big numbers flip to small fractions near 0, and small fractions flip to big numbers. Multiply a number by its reciprocal and you always get 1.
Plug x and -x into the same rule. Sometimes you get the same answer twice, that is even symmetry, a mirror across the y-axis. Sometimes you get opposite answers, that is odd symmetry, a half-turn spin around the origin.
The same mirror rule from Part 2 works on whole shapes, not just single points. Reflect every corner across the mirror line, then connect the dots. Pick the image that shows the true flip.
Opposites, absolute value, reciprocals, and reflections, all mixed together. Round decimal answers to two places.
Opposites fold across 0. Absolute value measures the fold. Reciprocals fold across 1, or -1, by flipping the fraction. And a graph is even or odd depending on what happens when you fold it at the y-axis or spin it around the origin. Four different mirrors, one idea: find the fold, then read off what lands on the other side.