Completing a symmetric figure
You are given half of a figure and the axis of symmetry. Your job: draw the other half so that the whole figure is line-symmetric. This is one of the favourite Year-4 tasks — it looks tricky at first, but with a clear procedure it becomes very satisfying.
The big idea
Every point on the given half has a mirror partner on the other side of the axis. The mirror partner sits:
- on the opposite side of the axis,
- at the same distance from the axis (measured perpendicularly),
- on the same line as the original, when you draw across the axis at a right angle.
Find the mirror partner of every important point, then join the partners up the same way the original was joined.
Step-by-step procedure on squared paper
- Mark the axis with a clear dashed or coloured line so you don't accidentally cross it.
- Pick the corners of the given shape one by one. They are the points that need partners.
- For each corner, count the squares from the corner to the axis (perpendicular to it).
- From the axis, count the same number of squares on the other side. Mark the new point — that's the mirror corner.
- Repeat until every corner has a partner.
- Connect the mirror points in the same order as the originals.
Tip: write a small number next to every original corner and the same number next to its mirror partner. This stops the join-up step from going wrong.
A worked example
Given: a half-arrow drawn to the left of a vertical axis. Corners at:
- A: 4 squares left of the axis, on the axis line itself.
- B: 4 squares left, 2 squares up.
- C: 2 squares left, 2 squares up.
- D: 2 squares left, 4 squares up.
- E: on the axis, 4 squares up.
Mirror partners (same distance on the right side, same vertical position):
- A → already on the axis, so it stays.
- B → 4 squares right, 2 up.
- C → 2 squares right, 2 up.
- D → 2 squares right, 4 up.
- E → already on the axis, stays.
Connect E–D–C–B–A on both sides, and you get the full arrow.
Axes that aren't vertical or horizontal
If the axis is slanted (45°, for example), the same idea works, but counting is harder on plain paper. Tip for diagonal axes on squared paper: every diagonal step counts as one along the axis and one across, so use tracing paper — trace the shape and the axis, flip the trace over the axis, and the new position shows you where the mirror half goes.
Common mistakes
- Counting from the wrong line. You always count from the axis, not from the edge of the page.
- Going only half-way. If a corner is 3 squares from the axis, its partner is 3 squares on the other side — so the total distance between original and mirror is 6 squares, not 3.
- Joining the points in the wrong order. Number the corners. The mirror order is the same as the original — A–B–C–D, mirror A'–B'–C'–D'.
- Missing a corner that lies on the axis. Points exactly on the axis are their own partner — they don't move.
What's next
- Lines of symmetry — count axes before you draw mirror halves
- Symmetry around us
- Back to the introduction