Reflections: identify the line and the order
Work through axis and diagonal mirrors, non-origin lines and rotation order. Complete examples for original coordinate practice, without ability bands.
This public guide explains one part of the original word-and-coordinate practice. Every complete attempt shows all five topic counts and all five full guides. It is not a private attempt, ranked outcome, percentile or general spatial-ability classification.
A mirror preserves distance to its line
Reflection places a point on the opposite side of the specified line at the same perpendicular distance. It is a whole transformation, not a general instruction to negate whichever coordinate looks convenient. A horizontal mirror keeps horizontal position and changes vertical position; a vertical mirror does the reverse. Diagonal mirrors combine the coordinate roles differently. Identify the actual line, including any nonzero offset, before using a formula. The grid remains fixed and the object is reflected within it, rather than the coordinate system being renamed.
A fresh non-origin mirror example
Reflect P(5,-2) across x=2. The point is three units to the right of that vertical line, so its partner lies three units left, at (-1,-2). The horizontal distances to the mirror match, while y stays unchanged. Reflecting the same original point across the x-axis instead gives (5,2). These are different operations with different lines. Merely seeing a minus sign in the starting coordinate does not tell you which sign should change or whether a translation of the mirror is involved.
Keep the two diagonals distinct
For the fresh point (5,-2), reflection in y=x exchanges coordinates and gives (-2,5). Reflection in y=-x exchanges and negates them, giving (2,-5). Applying either same reflection a second time returns the original point, which is a useful inverse check. That return does not make the two first images equal. Mark the diagonal or write its equation before computing so the correct coordinate rule stays attached to the specified line rather than to a remembered picture from another item.
Rotation and reflection generally do not commute
Start a new example at (2,4). Rotating 90° counterclockwise first gives (-4,2); reflecting that across the x-axis gives (-4,-2). Reversing the operations gives (2,-4) after reflection and then (4,2) after rotation. The endpoints differ. Keep an intermediate coordinate after every step, especially when the operations have different kinds or centres. A single shortcut chosen from the last verb can miss the entire effect of the earlier move even when each individual formula is familiar.
Compare full shapes under allowed moves
Matching one corner does not establish that two occupied-cell shapes are the same. Check every listed centre after the same allowed rotation and translation. A reflected shape sometimes matches its original set when the figure is symmetric, so do not use a universal claim that every mirror image is different. For the asymmetric L in this bank, all four permitted quarter-turn orientations can be compared explicitly. Keeping the short arm’s attachment point visible helps distinguish its mirror from a translated or rotated copy.
Use a sketch without changing the task
Sketch the mirror line and a perpendicular segment from the point to that line. Place the partner the same distance beyond it, then read the fixed coordinates. For a diagonal line, use the stated coordinate rule as a second check rather than judging by how a rough drawing looks. A map’s left side and an observer’s bodily left are different reference questions; neither should silently replace the line in a reflection task. Draw only what the wording supports, keeping point labels and operation order visible.
A six-item result is a revision record
The reflection count is a correct-answer count on these six written cases, not a diagnosis of perception, attention, handedness or general spatial ability. A missed option cannot by itself reveal whether the mirror line, offset or operation order caused the error. Read that item’s explanation and try a fresh case changing just one condition. All complete attempts receive all five guides, regardless of count. Paper is allowed and there is no timer, norm, percentile, hiring cut-off or evidence here of improvement beyond the fixed practice bank.