Problem
Flip across a line creates symmetry
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.
Geometry
Your answer
Watch out It's easy to treat this like flipping across a vertical or horizontal line, but reflecting over a diagonal swaps the across-and-up grid steps, not just one direction.
How to solve
Strategy Draw a Diagram — 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.
1STEP 1
Identify the mirror line
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.
4.G.A.3Draw A Diagram2STEP 2
Reflect each corner across the diagonal
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.
4.G.A.3Visualize Spatial RelationshipsEach corner of the figure reflects to a mirror point the same number of grid steps from the dashed line, on the opposite side.
Why?
Flipping the figure over the dashed line is the same as folding the grid along that line, so every corner is carried straight across the line to a matching spot on the far side.
Why?
In that fold the corner and the spot it lands on are pressed exactly on top of each other, and a fold keeps matched lengths equal, so both sit the same distance from the crease.
🧱Rigid motion preserves length and angleSliding, turning, or flipping a shape lays it exactly onto a copy, so every length and angle stays the same (folding is the flip case).
3STEP 3
Connect the mirrored corners
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.
4.G.A.3Draw A DiagramAnswer
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.
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.
Takeaway
Flipping across a line is just folding along it - mirror every corner the same distance to the other side!
- Identify the mirror line
- Reflect each corner across the diagonal
- Connect the mirrored corners
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