Virginia SOL 8.MG.3.f
The Standard
Sketch the image of a polygon that has been translated and reflected over the x- or y-axis, or reflected over the x- or y-axis and then translated.
Virginia Standards of Learning for Mathematics · The student will apply translations and reflections to polygons in the coordinate plane.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students track every vertex through a two-step move on a coordinate grid. They use translation vectors and axis-reflection rules, then connect the new points in the original vertex order.
What Mastery Looks Like
- Students accurately plot each intermediate image, label corresponding vertices, and draw the final polygon in the correct location and orientation. They use coordinate rules and explain why changing the order can change the result.
Common Misconceptions
- Students often change x for a reflection across the x-axis instead of changing y. They may reverse translation signs, skip the intermediate image, or assume the two steps give the same result in either order.
How to Assess It
- Plot triangle A(1, 1), B(3, 1), C(2, 3). Translate it left 2 and up 1, then reflect it across the y-axis, labeling both images.
Lesson moves
Ways to Teach It
On patty paper over a coordinate grid, students trace a polygon, slide it by a given vector, then flip it across an axis.
Show both transformation orders for one triangle and ask, “Why do the final coordinates differ, and when might they match?”
Run a transformation relay where teams draw translation and reflection cards, plot each intermediate image, and check a partner’s coordinates.
Have students design a tiled border by translating a small polygon motif and reflecting copies across horizontal or vertical centerlines.
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Related Standards
- 8.MG.3.d
Sketch the image of a polygon that has been translated vertically, horizontally, or a combination of both.
- 8.MG.3.e
Sketch the image of a polygon that has been reflected over the x- or y-axis.
- 8.MG.3.b
Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been reflected over the x- or y-axis
- 8.MG.3.c
Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated and reflected over the x- or y-axis or ref...
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