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About This Worksheet
A center of dilation is the fixed point where a figure grows larger or smaller during a transformation. This worksheet helps students study coordinate shapes and determine both the center of dilation and the scale factor. Students compare original figures and image figures to understand how distances change while shapes stay similar. For example, a small triangle may become a larger triangle that lines up with the same center point. The activity combines graph reading, coordinate reasoning, and geometric thinking in one lesson.
Curriculum and Grade Alignment
This worksheet supports transformation geometry and similarity concepts. The main learning goal is to identify how scale factors and centers of dilation affect figures on a coordinate plane. Students should already understand plotting points and comparing side lengths on a graph. The next step after this skill is proving similarity using transformations and proportional reasoning. This aligns with HSG-SRT.A.1 because students explain how dilations create similar figures.
Student Tasks
On this worksheet, students will study pairs of figures on a coordinate grid and determine the center of dilation for each set. They will compare image figures to original figures to identify the scale factor. Students also describe whether the figures represent enlargements or reductions. The chart at the bottom asks learners to organize their findings and compare the transformations.
Common Challenges and Misconceptions
Some students may think the center of dilation must always be the origin, even when it is not. Others may confuse the original figure with the image figure while comparing side lengths. A common mistake is counting grid spaces incorrectly when estimating distances from the center. Teachers can help by having students draw lines through matching vertices to locate the center point more clearly.
Implementation Guidance
This worksheet works well during lessons on similarity and geometric transformations. Teachers can model one example together before asking students to solve the remaining figures independently or with partners. Parents using this page at home can encourage students to explain why the shapes still look the same even after resizing. Talking through the movement helps students connect the graph to the math rule.
Details and Features
The worksheet includes large coordinate grids, color-coded figures, and organized answer tables. Students practice both enlargements and reductions in the same activity. The printable layout gives enough space for drawing lines, writing notes, and comparing shapes carefully. Visual examples support students who learn best through diagrams and hands-on graph work.