Mirror-Line Reflections

A mirror can move a whole shape without sliding it or turning it. Strange? Watch the corners... each one leaps across the line, yet stays exactly the same distance away.

A reflection is a flip across a mirror line. Imagine folding the grid along that line. Every corner lands directly opposite its starting point. The line sits halfway between the old corner and its image. So count the perpendicular squares to the line, then count the SAME number beyond it. For a vertical mirror line, move left or right, never up or down. For a horizontal mirror line, move up or down, never sideways. Plot each image corner carefully. Join the image corners in the same order, and the reflected shape appears. Coordinates are always read across first, then up. Do not swap them. And do not spin the shape as if it were turning. A reflection FLIPS it. Any corner on the mirror line stays fixed.

Let's work through an example. On a square coordinate grid, triangle A B C has corners A at two, one; B at four, one; and C at three, four. The mirror line is the vertical line x equals six. Reflect triangle A B C in that line, and give the coordinates of its three image corners. Start with A at two, one. Its horizontal distance to x equals six is four squares. Cross the line by four squares. A prime lands at ten, one. Notice that the second coordinate stays one. Now B is at four, one. It is two squares from the line, so B prime lands at eight, one. Finally, C is at three, four. Count three squares horizontally to the mirror line, then three beyond it. C prime lands at nine, four. Join A prime, B prime, and C prime. The completed image is triangle A prime B prime C prime, with corners ten, one; eight, one; and nine, four.

Reflect corner by corner: count to the mirror line, count equally beyond, then join. Across first, then up. You can spot the true mirror image!