Free printable resources · Original practice
Reflect original geometric motifs across a marked axis. Six vertical and six horizontal exercises make every matching corner countable on the grid.
The complete collection
Download the student pack for practice and the separate answer pack to compare. Individual editable sheets appear below. The paper-size choice applies to every download button.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
| Mirror line | Point | Reflected point |
|---|---|---|
| x = 0 (vertical axis) | (-3, 2) | (3, 2) |
| y = 0 (horizontal axis) | (2, -4) | (2, 4) |
| x = a (general rule) | (x, y) | (2a − x, y) |
| y = b (general rule) | (x, y) | (x, 2b − y) |
Join the reflected vertices in the same sequence as the original half. The dark axis remains fixed. An endpoint on the axis is shared by both halves; do not draw a second shifted endpoint. The answers use brown for the added half so you can compare corresponding segments.
Begin by identifying the specific axis provided on the worksheet, whether it is a vertical line defined by x equals a or a horizontal line defined by y equals b. This line acts as the mirror for the geometric or simplified plant and animal outlines. It is crucial to recognize that any point lying directly on this axis remains fixed and does not move during the reflection process. Students must carefully observe the single half of the shape presented on the grid. Understanding that the axis is the boundary between the original and reflected halves helps prevent common errors. By anchoring the reflection to this fixed line, learners can accurately determine where each corresponding point on the opposite side should be placed to maintain symmetry.
Use the mathematical formulas to calculate the exact position of each reflected point. For a vertical axis at x equals a, the new x coordinate is calculated as two a minus the original x, while the y coordinate remains unchanged. For a horizontal axis at y equals b, the x coordinate stays the same, and the new y coordinate is two b minus the original y. This method ensures precision beyond simple visual estimation. Students should apply these rules to every vertex of the shape. By systematically transforming each coordinate pair, the reflected half is constructed with mathematical accuracy, ensuring the final image is a true mirror image rather than a distorted approximation of the original outline.
After plotting the reflected points, verify the distance from the axis using perpendicular grid intervals. For vertical reflections, the horizontal distance from the axis must be identical on both sides, while the vertical height remains preserved. For horizontal reflections, the vertical distance from the axis must match, while the horizontal position stays constant. Ensure the scale remains consistent on both sides of the grid. A common error is copying the shape via translation instead of reflecting it. By counting grid squares perpendicular to the axis, students confirm that the reflected half is correctly positioned. Matching each corresponding vertex checks the intended bilateral symmetry of these straight-segment outlines.
| Watch for | Check instead |
|---|---|
| Translating the shape instead of reflecting it | Ensure points are mirrored across the axis, not shifted sideways or up. Use the formula two a minus x for vertical axes to find the correct horizontal position. |
| Ignoring points on the axis of symmetry | Remember that points lying directly on the vertical or horizontal axis stay fixed. Do not move these vertices when drawing the reflected half of the shape. |
| Inconsistent scaling between original and reflected halves | Maintain the same grid scale on both sides. Count perpendicular intervals carefully to ensure the distance from the axis is identical for corresponding points. |
Before you begin
No. This collection uses original straight-segment motifs so every corner can be checked by counting intervals. Keep the corners rather than smoothing them into a new shape.
Each sheet has a dark vertical or horizontal axis through the center of the grid. Treat that line as coordinate zero for the reflection example. The original half is dark and the added half is brown in the answer.
The different shades distinguish the original half provided on the worksheet from the reflected half you draw. This visual separation helps verify that the reflection is complete and correctly positioned.
Yes. Every linked PDF, SVG, worksheet and answer is free without signup. The original resources use CC BY 4.0: credit Zumola, link the license and indicate changes. Analytics consent is not required to download or use the resources.
Treat the symmetry axis as a line on the grid. For a vertical axis at column x = a, a point at (x, y) reflects to (2a - x, y). For a horizontal axis at row y = b, a point at (x, y) reflects to (x, 2b - y). These formulas work for every vertex, so you can check corners one at a time instead of trusting the overall outline.
Distances stay the same under reflection: a segment 3 squares long stays 3 squares long, and a right angle stays a right angle. Area is unchanged too, so a half-shape covering 6 grid squares should produce a completed shape covering 12. If your count differs, a vertex has probably been placed on the wrong square.
Suppose the vertical axis sits at column 4 and the given half has vertices at (1, 1), (3, 1), (3, 3), and (1, 3). Using x' = 8 - x, the reflected vertices are (7, 1), (5, 1), (5, 3), and (7, 3). Joining them in matching order gives a rectangle mirrored to the right of the axis.
The original half covers 4 grid squares, so the completed shape should cover 8. Each horizontal edge is 2 squares and each vertical edge is 2 squares on both sides. If a reflected corner lands one square off, the formula shows exactly which coordinate is wrong.
Art has more than one valid outcome, so judge the reflection against stated criteria rather than a single correct picture. A completed half can look slightly different from another student's and still be accurate if every vertex mirrors correctly and the axis is respected.
Use the rubric below to score a page consistently. It separates geometric accuracy from neatness, so a wobbly but correctly placed line is not penalised as a reflection error.
Completing a half is a drawing task: the goal is a correctly reflected outline. Judging whether a finished shape is symmetrical, calculating its area, or applying a second reflection are different tasks with different checks. Keep them apart so a drawing error is not confused with a measurement error.
When a page asks for area, state the unit, such as square centimetres or grid squares. When it asks for angles, give degrees. Mixing these up makes an otherwise correct reflection look wrong.
A horizontal axis sits at row 5. A given half has vertices at (2, 2), (4, 2), and (4, 4). Find the reflected vertices and the completed shape's area in grid squares.
Using y' = 10 - y, the reflected vertices are (2, 8), (4, 8), and (4, 6). The given half is a right triangle covering 2 grid squares, so the completed shape covers 4 grid squares. Each vertical edge of 2 squares mirrors to 2 squares, and the horizontal edge of 2 squares stays 2 squares.
Count squares from each vertex to the axis and confirm the mirrored vertex is the same number of squares away on the opposite side, at the same height or column.
No. Any outline whose vertices mirror correctly across the marked axis is valid; small differences in line neatness do not change the geometry.
The simple column or row formulas do not apply. A diagonal axis needs a different reflection rule, so treat it as a separate task and check distances along perpendicular lines.
