Dilation Properties

Pre-Algebra · Axiom Academy

One number, the scale factor k , controls a dilation: it grows or shrinks a figure away from a fixed center while every angle stays exactly the same. 1. The Scale Factor Sets the Size The scale factor k is a single multiplier applied to the figure. Watch the same triangle shrink, return, and grow as k runs from a half, up through one, to two — and read the live value as it changes. k > 1 — enlargement (the figure gets bigger) 0 < k < 1 — reduction (the figure gets smaller) Every dilation has a center that acts like an anchor. Lines run from the center through each vertex, and the whole figure slides along those lines. Watch the center hold perfectly still while the triangle pushes outward to k = 2 . Stays exactly where it is — it is its own image. Moves along the straight line from the center through it. Move more than nearby points — they have farther to travel. k > 1 pushes outward; 0 < k < 1 pulls inward. 3. Distances Scale by k — Angles Don't Here is the precise property. The distance from the center to a point is multiplied by k , so a point twice as far out lands twice as far out. Yet the figure's angles never change — the image is the same shape, just resized. Watch one corner's distance from the center stretch to while its angle holds steady. distance from center is multiplied by the scale factor Side lengths and distances from the center — all multiplied by k . Every angle, and therefore the overall shape. The image is similar to the original.

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