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Use a marked mirror axis to complete a half-drawn car on grid paper, square by square. Practice precise symmetry, counting, and checking with a simple convention.
This lesson teaches grid-based mirror symmetry by completing the right half of a car whose left half is already drawn on graph paper. You will count squares from the mirror axis, plot matching points on the opposite side, and connect them to form a clean silhouette. The focus is the mirrored outline only: no freehand car construction, perspective, or mechanical detail. A simple convention makes every step checkable: each grid intersection is a point, and the mirror axis is a vertical line through grid intersections. Because letter styles and drawing styles vary, the rubric accepts any valid mirrored outline that follows the convention, not one universal shape.
Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.
Place the graph-paper sheet so the vertical mirror axis runs through grid intersections. Label the axis x = 0. Count columns to the right as +1, +2, +3 and to the left as -1, -2, -3. Each small square is one unit. The left half of the car is already drawn on the left side; the right half is blank.
Before drawing, list the key outline points on the left half as coordinate pairs (column, row). Use rows counted upward from a chosen baseline row, labelled y = 0. For example, a point three columns left of the axis and two rows above the baseline is (-3, 2).
For a vertical mirror axis at x = 0, the mirror of a point (x, y) is (-x, y). The row stays the same; only the column sign changes. A point at (-4, 3) mirrors to (4, 3). A point on the axis, such as (0, 5), mirrors to itself.
Work one point at a time and mark the mirrored point with a small dot. Keep the original list beside you so you can compare counts. If a left point is two squares from the axis, its mirror must be two squares from the axis on the right.
Join the mirrored dots in the same order as the left-half outline. Use straight grid segments between neighbouring points. Where the left outline meets the axis, the right outline must meet the same axis point so the two halves join without a gap or overlap.
After connecting, trace the full silhouette once. The car should look balanced about the axis. Small style choices, such as whether a wheel arch is drawn with two or three segments, are acceptable if the mirrored side matches exactly.
Checking is counting. For each marked point on the right, count squares back to the axis and compare with the matching left point. The counts must be equal. Also compare rows: a point three rows above the baseline on the left must be three rows above on the right.
A useful check is to fold the sheet along the axis if the paper is thin, or to hold a straight edge on the axis and compare distances. Do not rely on appearance alone; use the coordinate list.
A left-half outline has points (-5, 1), (-3, 4), (-1, 6), and (0, 6). The mirror axis is x = 0. Find the mirrored points and describe how to connect them.
The mirrored points are (5, 1), (3, 4), (1, 6), and (0, 6). Connect them in the same order as the left half, joining at the shared axis point (0, 6). Check that each right point is the same number of squares from the axis and on the same row as its left partner.
Mirror the points (-4, 2), (-2, 5), and (0, 7) across the vertical axis x = 0. List the mirrored points.
(4, 2), (2, 5), (0, 7).
Why: For a vertical axis at x = 0, change the sign of the column only. The row stays the same. The point on the axis mirrors to itself.
Check: Count squares from the axis: each mirrored point must be the same distance from the axis and on the same row as its partner.
A left-half outline includes a point at (-3, 4). A student marks the mirror at (3, 5). Explain the error and give the correct point.
The row was changed. The correct mirror is (3, 4).
Why: Mirroring across a vertical axis keeps the row unchanged. Only the column sign changes, so (-3, 4) becomes (3, 4).
Check: Compare rows: both points must be on row 4. Count three squares from the axis on each side.
The left half has outline points (-6, 1), (-4, 3), (-2, 3), and (0, 5). Mirror them and state the order in which to connect the right-half points.
Mirrored points: (6, 1), (4, 3), (2, 3), (0, 5). Connect in the order (6, 1) to (4, 3) to (2, 3) to (0, 5), joining at the shared axis point (0, 5).
Why: Each point mirrors by changing the column sign. The connection order follows the left-half sequence so the outline shape matches.
Check: Verify each pair has equal distance from the axis and the same row, and that the final segment ends at the shared axis point.
A completed right half has points (2, 3), (4, 3), and (5, 1). The left half has (-2, 3), (-4, 3), and (-5, 1). A checker says the outline is correct. Is the checker right? Give a reason.
Yes. Each right point is the exact mirror of the corresponding left point: same row and equal distance from the axis.
Why: The pairs are (-2, 3) with (2, 3), (-4, 3) with (4, 3), and (-5, 1) with (5, 1). All satisfy the mirror rule.
Check: Count squares from the axis for each pair and compare rows. All counts and rows match.
No. The left half is already drawn. Your task is to complete the right half by mirroring the existing outline on the grid.
That is acceptable if your right half is an exact mirror of your left half under the stated convention. The rubric checks symmetry and grid accuracy, not one universal car shape.
Every outline point should sit on a grid intersection. Count squares carefully; a one-square error will show as an unequal distance from the axis.
This task is limited to the mirrored silhouette. Additional mechanical detail is outside the brief and is not required.