Virginia SOL Math / Grade 7 / Measurement & Geometry

7.MG.4

Dilations on the Coordinate Plane

What you'll learn

  • Dilate a polygon from the origin using a scale factor
  • Find the coordinates of an image after a dilation
  • Describe how a dilation changes size but not shape

Words to know

Dilation —
a transformation that enlarges or reduces a figure
Scale factor —
the number that multiplies each coordinate in a dilation
Preimage —
the original figure before a transformation
Image —
the new figure after a transformation
Origin —
the point (0, 0) where the axes cross

Why it matters Dilations model zooming in and out, resizing photos, and scaling drawings while keeping the same shape.

Worked examples

Model ItI do

Dilate the point (2, 3) from the origin by a scale factor of 2.

Multiply each coordinate by the scale factor: 2 times 2 = 4 and 3 times 2 = 6. The image is (4, 6).

Try It TogetherWe do

Dilate the point (6, 4) from the origin by a scale factor of one half.

Multiply each coordinate by one half: 6 times one half = 3 and 4 times one half = 2. The image is (3, 2), a smaller figure.

Now YouYou do

Dilate the point (1, 5) from the origin by a scale factor of 3.

Multiply both coordinates by the scale factor. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Dilate the point (2, 4) from the origin by a scale factor of 2.

  2. 2.Dilate the point (6, 8) from the origin by a scale factor of one half.

  3. 3.Does a scale factor of 3 make a figure larger or smaller?

On Level

The core Quick Check from the book.

  1. 1.Dilate (3, 2) from the origin by a scale factor of 2.

  2. 2.Dilate (4, 8) from the origin by a scale factor of one half.

  3. 3.A scale factor greater than 1 makes a figure larger or smaller?

  4. 4.Dilate (5, 0) from the origin by a scale factor of 3.

  5. 5.Dilate (2, 6) from the origin by a scale factor of one third.

Challenge

Stretch your thinking.

  1. 1.A triangle has vertices (1, 2), (3, 0), and (2, 4). Dilate it from the origin by a scale factor of 3. Give the three image points.

  2. 2.Dilate the point (9, 6) from the origin by a scale factor of one third.

  3. 3.After a dilation from the origin, the point (2, 5) maps to (8, 20). What scale factor was used?