Illustrative Math Lesson

Zooming In and Out: Exploring Dilations on the Coordinate Plane

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8th GradeBTC Style / Thinking ClassroomsCCSS.MATH.CONTENT.8.G.A.3, CCSS.MATH.CONTENT.8.G.A.440 min

Learning Objective

Students will be able to perform dilations of polygons on the coordinate plane given a center of dilation and a scale factor, and describe the relationship between pre-image and image coordinates.

Lesson Overview

Students progress from identifying scale factors in simple dilations centered at the origin to applying dilations with non-origin centers and fractional scale factors, building understanding of how dilation preserves shape while changing size.

Materials

Vertical whiteboards or chart paper
Dry-erase markers (multiple colors)
Pencils and paper for scratch work
Basic calculator or phone calculator

Scaffolded Task Progression

1Task 1

Point

P = (3, 5)

is dilated from the origin with a scale factor of

2

. What are the coordinates of P', the image of

P

?

Then dilate

Q = (4, 1)

from the origin with scale factor

2

. What is Q'?

What pattern do you notice?

2Task 2

Triangle

A B C

has vertices

A = (1, 2)

B = (3, 2)

C = (3, 5)

. Dilate it from the origin with scale factor

k = 3

.

1. Find A', B', C'.
2. On your whiteboard, sketch both triangles on a coordinate grid.
3. Draw rays from the origin through each pair (A, A'), (B, B'), (C, C'). What do you notice about those rays?

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