Virginia SOL 8.MG.3.c
The Standard
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 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 each vertex through two transformations in the given order. They use reflection and translation rules, then list the final coordinates of the polygon.
What Mastery Looks Like
- A student applies the first rule before the second to every vertex. They label corresponding vertices, report accurate ordered pairs, and check that side lengths remain unchanged.
Common Misconceptions
- Students often reverse the transformation order, change only one coordinate during a translation, or use the wrong sign in a reflection. They may negate x when reflecting across the x-axis or lose vertex correspondence.
How to Assess It
- Exit ticket: Triangle A(1, 2), B(4, 2), and C(2, 5) is reflected across the y-axis, then translated 3 units right and 1 unit down. List all intermediate and final coordinates.
Lesson moves
Ways to Teach It
Plot a polygon on graph paper, trace it on patty paper, reflect it across an axis, then slide it by a given vector.
Compare reflection-then-translation with translation-then-reflection for one triangle, and write why the final coordinates match or differ.
Give pairs coordinate-rule cards and polygon cards; partners race to calculate each image, then check by plotting.
Map a logo's vertices, mirror it across a storefront centerline, then shift the copy to create a balanced window display.
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Related Standards
- 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.a
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- 8.MG.3.f
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- 7.MG.4.a
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