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Shrinking a Shape

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 21 of 60.

A scale factor between 0 and 1 shrinks the shape. Every point moves towards the center, to a fraction of its distance.

$Triangle PQR shrunk by one third towards the origin$

Here k = $\frac{1}{3}$ . P(3, 6) goes to P'(1, 2) and Q(6, 3) to Q'(2, 1): each coordinate is divided by 3. The image is a third of the size, and still the same shape. A scale factor bigger than 1 enlarges, exactly 1 changes nothing, and between 0 and 1 shrinks.

Challenge

Draw the image of triangle ABC after the dilation by $\frac{1}{2}$ about the origin. Drag A', B' and C' into place, then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image The Translation Rule Recap: Translations

4Combining Moves

One Move, Then Another Order Matters Two Mirrors Name the Move Recap: Combining Moves

7Drawing on Squared Paper

Lengths by Pythagoras Perpendicular Steps Squares by Area Right Triangles by Area Midpoints on the Grid Recap: Squared Paper

10Perpendiculars and Parallels

Perpendicular From a Point Perpendicular at a Point Parallel Through a Point Tools You Have Earned Recap: Parallels

2Reflections

Reflecting in a Line The Two Axes The Line y = x Find the Mirror Recap: Reflections

5Dilations

Scaling From a CenterShrinking a ShapeDilating About a Point Negative Scale Factors Recap: Dilations

8Compass and Straightedge

Circles Keep Distances Why the Sides Match Angles You Built A 60° Angle Recap: Equilateral Triangle

11Constructed Shapes

A Square on a Segment The Regular Hexagon Copy an Angle A Tangent From a Point Recap: Constructed Shapes