Grades 3–5 · Mathematics
What makes two sides reflection-symmetric?
Reflection symmetry means that a pattern matches its mirror image across a line. Folding a flat pattern along that line is a useful way to picture the match: corresponding points would land together.
In the diagramReflection needs matching positionsGrid spacing = 1 unit · vertical mirror lineMirror lineAA′BB′CC′All 3 pairs match across the line.Distances to the mirror are measured at right angles.
The line in this grid is vertical. A reflected partner must therefore be on the same row as its original point and the same distance from the line on the other side. The distance is measured straight across at a right angle to the mirror line, not along a slanted path.
The initial pattern contains three matching pairs. The top and bottom pairs are each two grid intervals from the line, and the middle pair is one interval away. Each partner has the required row and distance.
Having three dots on each side is not enough on its own. A dot could be too far from the line or at the wrong height. Reflection symmetry depends on the positions of every corresponding pair, not just equal counts.
About this explanation
Starting knowledge: Count small grid intervals and recognize horizontal, vertical and right-angle directions.
Sources
- Common Core State Standards Initiative — Grade 4 Geometry: Lines of symmetry (4.G.A.3)
- University of Cambridge, NRICH — Let Us Reflect