8.10.C
The Standard
explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use algebraic coordinate rules to move, flip, or rotate two-dimensional figures on a coordinate plane. They explain how each rule changes the x- and y-coordinates and identify the resulting transformation.
What Mastery Looks Like
- Students correctly apply coordinate rules to every vertex and graph the image. They identify the transformation, state its direction or angle, and explain how coordinates change while size and shape stay fixed.
Common Misconceptions
- Students may switch the rules for reflecting across the x-axis and y-axis. They may also reverse translation signs or use the wrong coordinate order in rotation rules.
How to Assess It
- Give students triangle vertices A(1, 2), B(4, 2), and C(2, 5). Ask them to apply (x, y) → (-y, x), graph the image, and explain the change.
Lesson moves
Ways to Teach It
Plot a paper triangle on a coordinate mat, then slide, flip, and turn it while recording each vertex before and after.
Ask students to explain in writing why reflecting (3, -5) across the x-axis changes only one coordinate.
Play a rule-matching game with cards showing coordinate rules, transformation names, graphs, and matching image coordinates.
Use a simple floor plan to reposition a table by translation, reflect a design feature, and rotate a rug around the origin.
Keep exploring
Related Standards
- 8.3.B
compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane
- K.6.D
identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably
- 8.3.C
use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with th...
- 8.10.A
generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.