Virginia SOL Math / Geometry / Reasoning, Lines & Transformations

G.RLT.3

Symmetry & Transformations

What you'll learn

  • Identify line symmetry and rotational symmetry in figures
  • Perform reflections, translations, and rotations on the coordinate plane
  • Determine the coordinates of an image after a transformation

Words to know

Transformation —
a change in a figure's position or size
Reflection —
a flip over a line
Translation —
a slide with no turning
Rotation —
a turn about a fixed point
Line of symmetry —
a line that divides a figure into mirror halves

Why it matters Symmetry and transformations describe how patterns repeat and how objects move, from tile designs to animation and robotics.

Worked examples

Model ItI do

Triangle A is reflected across the dashed vertical line to form A'. Describe what stays the same and what changes.

A reflection is a flip, so A' is the mirror image of A. The side lengths and angle measures stay the same (the triangles are congruent), but the orientation is reversed: what pointed right now points left.

Try It TogetherWe do

Point P(3, 4) is translated 5 units left and 2 units down. Find the image P'.

Left subtracts from x, down subtracts from y: P' = (3 - 5, 4 - 2) = (-2, 2).

Now YouYou do

Point Q(2, -5) is reflected across the x-axis. Find the image Q'.

Reflecting across the x-axis keeps x and negates y. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Reflect the point (3, 5) across the y-axis. Give the image.

  2. 2.How many lines of symmetry does a square have?

  3. 3.Does a translation change a figure's size?

On Level

The core Quick Check from the book.

  1. 1.Reflect the point (4, 1) across the y-axis. Give the image.

  2. 2.Translate (0, 0) by 3 right and 6 up. Give the image.

  3. 3.How many lines of symmetry does a square have?

  4. 4.Does a translation change a figure's size?

  5. 5.Reflecting (5, -3) across the x-axis gives which point?

Challenge

Stretch your thinking.

  1. 1.Point A(4, -2) is reflected across the x-axis, then translated 3 units right. Find the final image.

  2. 2.Point B(2, 3) is rotated 90 degrees counterclockwise about the origin. Find the image.

  3. 3.Point C(-5, 6) is rotated 180 degrees about the origin. Find the image.