Dilations on the Coordinate Plane

Examples, videos, and solutions to help Grade 8 students learn how to describe the effect of dilations on two-dimensional figures using coordinates.

New York State Common Core Math Grade 8, Module 3, Lesson 6

Worksheets for Grade 8

Lesson 6 Student Outcomes

• Students describe the effect of dilations on two-dimensional figures using coordinates.

Lesson 6 Summary

Dilation has a multiplicative effect on the coordinates of a point in the plane. Given a point (x, y) in the plane, a dilation from the origin with scale factor r moves the point (x, y) to (rx, ry)
For example, if a point (3, -5) in the plane is dilated from the origin by a scale factor of r = 4, then the coordinates of the dilated point are (4 × 3, 4 × (-5)) = (12, - 20)

NYS Math Module 3 Grade 8 Lesson 6

Classwork
Example 1
Students learn the multiplicative effect of scale factor on a point. Note that this effect holds when the center of dilation is the origin. In this lesson, the center of dilation will always be assumed to be (0, 0)

Example 2
Students learn the multiplicative effect of scale factor on a point.

Example 3
The coordinates in other quadrants of the graph are affected in the same manner as we have just seen. Based on what we have learned so far, given point A = (-2. 3) predict the location of A’ when A is dilated from a center at the origin, (0, 0) by scale factor r = 3.

Exercises 1 - 5

1. Point A = (7, 9) is dilated from the origin by scale factor r = 6. What are the coordinates of point A'?
2. Point B = (-8, 5) is dilated from the origin by scale factor r = 1/2. What are the coordinates of point B'?
3. Point C = (6, -2) is dilated from the origin by scale factor r = 3/4. What are the coordinates of point C'?
4. Point D = (0, 11) is dilated from the origin by scale factor r = 4. What are the coordinates of point D'?
5. Point E = (-2, -5) is dilated from the origin by scale factor r = 3/2. What are the coordinates of point E'?

Example 4
Students learn the multiplicative effect of scale factor on a two dimensional figure.

Example 5
Students learn the multiplicative effect of scale factor on a two-dimensional figure.

Exercises 6 - 8
6. The coordinates of triangle ABC are shown on the coordinate plane below. The triangle is dilated from the origin by scale factor r = 12. Identify the coordinates of the dilated triangle A’B’C’.
7. Figure DEFG is shown on the coordinate plane below. The figure is dilated from the origin by scale factor r = 2/3. Identify the coordinates of the dilated figure D’E’F’G’, then draw and label figure D’E’F’G’ on the coordinate plane.
8. The triangle ABC has coordinates (3, 2) (12, 3) and (9, 12). Draw and label triangle ABC on the coordinate plane. The triangle is dilated from the origin by scale factor r = 1/3. Identify the coordinates of the dilated triangle A’B’C’, then draw and label triangle A’B’C’ on the coordinate plane.

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