Dilations In The Coordinate Plane: Common Core Geometry Homework Answers

Understanding dilations on the coordinate plane is a core component of the Common Core Geometry curriculum. Students often seek clear explanations and step‑by‑step solutions for homework assignments that ask them to find scale factors, write transformation rules, and graph dilated figures. This article provides a concise guide to mastering dilations, complete with practical examples and tips for locating reliable answers.

What Is a Dilation?

A dilation is a transformation that produces a figure similar to the original by enlarging or reducing distances from a fixed point called the center of dilation. In the coordinate plane, the center is usually the origin (0, 0) or another point (h, k). The size change is determined by the scale factor k:

Every point (x, y) of the original figure maps to a new point (k·x, k·y) when the center of dilation is the origin. When the center is (h, k), the rule becomes (h + k·(x − h), k + k·(y − k)).

Finding the Scale Factor

Homework problems often give you two corresponding points before and after dilation. To find the scale factor, compare the distances from the center to each point. For example, if (2, 3) dilates to (6, 9) with the origin as the center, compute:

  1. Original distance: √(2² + 3²) = √13.
  2. Image distance: √(6² + 9²) = √(36 + 81) = √117.
  3. Scale factor k = √117 / √13 = 3.

Because each coordinate triples, the rule is simply (x, y) → (3x, 3y). This method aligns with the lesson “Join me as I show you how to find the scale factor and write a rule for …”.

Writing the Dilations Rule

Once the scale factor is known, express the transformation as a function. Use the format:

For a dilation with center (2, ‑1) and scale factor ½, the rule becomes (x, y) → (2 +