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Negative Scale Factors

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 24 of 61.

A scale factor can be negative. Then each point goes through the center and out the other side, to the size of k times its distance. The image is scaled and also turned upside down.

$Segment PQ dilated by negative 3 through the origin$

With k = -3 about the origin, P(1, 2) goes to (-3, -6): on the other side of O and 3 times as far. Q(2, 1) goes to (-6, -3). Lengths are multiplied by 3, the size of k, never by a negative number. A dilation by -1 sends (x, y) to (-x, -y): it is exactly the half turn.

Challenge

Find the dilation about the origin that takes triangle ABC onto the dashed target, apply it, 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 Image Coordinates 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 Center Shrinking a Shape Dilating About a PointNegative Scale FactorsRecap: 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