Scaling From a Center
Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 21 of 61.
A dilation enlarges or shrinks a shape from a center by a scale factor k. Each point slides along the ray from the center to k times its distance. About the origin that is simple: multiply both coordinates by k, so (x, y) → (kx, ky).
Here k = 3. P(1, 1) goes to P'(3, 3), three times as far from O along the same ray. Every length triples: PQ is 1 and P'Q' is 3. The angles stay exactly the same, so the image is the same shape at a new size. It is similar to the original, not congruent.
On the board, the move is Dilate: type k and keep the center at the origin unless the task says otherwise.
Challenge
Find the dilation about the origin that takes triangle ABC onto the dashed target: set the scale factor, press Apply, then press Check.
Try it yourself
Move the shape onto its target
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Transformations & Constructions
7Drawing on Squared Paper
Lengths by PythagorasPerpendicular StepsSquares by AreaRight Triangles by AreaMidpoints on the GridRecap: Squared Paper10Perpendiculars and Parallels
Perpendicular From a PointPerpendicular at a PointParallel Through a PointTools You Have EarnedRecap: Parallels5Dilations
Scaling From a CenterShrinking a ShapeDilating About a PointNegative Scale FactorsRecap: Dilations8Compass and Straightedge
Circles Keep DistancesWhy the Sides MatchAngles You BuiltA 60° AngleRecap: Equilateral Triangle