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Dilating About a Point

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 23 of 61.

When the center is not the origin, work from the center, as with rotations. Take the step from the center to the point, multiply the step by k, then add it back to the center.

$P dilated by 3 from the center C, along the ray from C$

Dilate P(4, 3) by 3 about C(1, 1). From C to P is ⟨3, 2⟩. Three times that is ⟨9, 6⟩, and C plus ⟨9, 6⟩ is P'(10, 7). The center, the point and its image always lie on one line, and the center is the one point that does not move.

Challenge

Triangle ABC is dilated by 2 about the point (2, -1). Write the coordinates of A', B' and C', 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 ShapeDilating About a PointNegative 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