Flip across a line creates symmetry

4.G.A.3 · take · grade 4

Archetype: Transformations Preserve Measures · step in a 8-type progression

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. The figure is an asymmetric shape made of a slanted line with one inward bend and a vertical edge. Draw the figure flipped across this dashed line.

Show solution

Understand

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure drawn below the line: a slanted segment with one inward bend plus a vertical edge.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each point of the reflected figure is the same perpendicular distance from the line as the original, on the opposite side.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex of the figure maps to a mirror point the same distance across the diagonal line. Drawing the diagram and visualizing the fold across the dashed line lets us place every corner of the reflected figure exactly.

Execute

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right of the grid (a diagonal at 45 degrees). Reflecting across it swaps the two sides: points below-right of the line move to above-left, and vice versa.

A diagonal fold line is just like folding paper along that crease so the two halves meet.

#17 Visualize Spatial Relationships 4.G.A.3

For a 45-degree diagonal, reflecting a point essentially swaps its 'across' and 'up' grid steps measured from the line. Take each vertex of the figure (the ends of the slanted segment, the inward bend, and the vertical edge) and mark its mirror point an equal number of grid steps on the opposite side of the dashed line.

Counting equal grid steps to the other side of the fold places each corner precisely.

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure. The result sits above the diagonal line, and the original-plus-reflection together are symmetric about the dashed line.

If the figure had been on the line it would overlap itself; the reflection mirrors it neatly across the crease.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side of the line, with the slanted segment, inward bend, and vertical edge all mirrored so the original and the reflection are symmetric about the dashed line.

Review

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent (same size and shape) to the original - exactly what a flip must produce.

Create a physical representation (tool 10): trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands exactly where the reflected figure should be drawn.

Standards · min grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡 Flipping across a line is just folding along it - mirror every corner the same distance to the other side!