What is Symmetric about a point? — Mathematics

Definition 52.1 Primary & Middle School Mathematics · Chapter 52 — Central Symmetry and Parallelograms

The symmetric of a point $M$ about a point $O$ is the point $M'$ such that $O$ is the midpoint of $[MM']$ . The symmetric figure is what the original becomes after a half-turn ( $180^\circ$ ) around $O$ .

Symmetry about O: each point and its image are aligned with O, at equal distances on both sides (tick marks). — Symmetry about $O$ : each point and its image are aligned with $O$ , at equal distances on both sides (tick marks).

Examples

Example 52.3 (On a grid)

If $M$ is $3$ squares left and $1$ square up from $O$ , its symmetric $M'$ is $3$ squares right and $1$ square down from $O$ : central symmetry reverses both directions at once (a reflection reverses only one).

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