Virginia SOL Math / Grade 8 / Measurement & Geometry

8.MG.3

Translations & Reflections

What you'll learn

  • Apply translations and reflections to figures on the coordinate plane
  • Identify the coordinates of an image after a transformation
  • Describe a transformation given a figure and its image

Words to know

Transformation —
a change in the position of a figure
Translation —
a slide of a figure without turning or flipping
Reflection —
a flip of a figure over a line
Preimage —
the original figure before a transformation
Image —
the figure that results after a transformation

Why it matters Transformations describe how objects move and flip, which matters in animation, tiling, and design on a grid.

Worked examples

Model ItI do

Translate the point (2, 5) by 3 units right and 4 units down.

Right adds to x and down subtracts from y. New x is 2 + 3 = 5, new y is 5 - 4 = 1. The image is (5, 1).

Try It TogetherWe do

Reflect the point (4, -3) over the x-axis.

A reflection over the x-axis keeps x and negates y. So (4, -3) maps to (4, 3).

Now YouYou do

Reflect the point (-2, 6) over the y-axis.

A reflection over the y-axis negates x and keeps y. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Translate the point (3, 2) by 4 units right. What is the image?

  2. 2.Reflect the point (5, 6) over the x-axis.

  3. 3.Which transformation slides a figure without turning it: a translation or a reflection?

On Level

The core Quick Check from the book.

  1. 1.Translate (1, 1) by 5 units right. What is the image?

  2. 2.Reflect (3, 7) over the x-axis.

  3. 3.Reflect (-5, 2) over the y-axis.

  4. 4.Translate (0, 4) down 6 units.

  5. 5.Which transformation flips a figure over a line: a translation or a reflection?

Challenge

Stretch your thinking.

  1. 1.The point (2, 5) is translated 3 units left and 6 units down, then reflected over the x-axis. Give the final image.

  2. 2.A triangle has a vertex at (4, -2). It is reflected over the y-axis. Where does that vertex land?

  3. 3.The point (6, 3) becomes (1, 3) after a transformation. Describe the transformation.