Graph Resize
About This Worksheet
A coordinate dilation is a resizing of a figure on a graph using a scale factor. This grade 10 geometry worksheet asks students to find original and new coordinates for dilated figures. Students compare shapes before and after the dilation so they can see how the rule changes every point. For example, (6, 4) becomes (3, 2) when the scale factor is one-half.
Curriculum and Grade Alignment
This worksheet is built for grade 10 students working with transformations on the coordinate plane. The main goal is to use scale factors to find image coordinates and compare related figures. Students should already know how to plot points, name coordinates, and read a grid. The next skill is using these coordinate changes to explain similarity and proportional side lengths. This aligns with Common Core HSG-SRT.A.1 because students describe what dilations do to figures.
Student Tasks
On this worksheet, students will record original coordinates and calculate new coordinates after a dilation. They will label image points and compare the original figure with the resized figure. Students will identify scale factors by studying how the coordinates or side lengths changed. They will also use the graph to check whether the image is an enlargement or a reduction.
Common Challenges and Misconceptions
Students may forget that a scale factor of one-half makes the figure smaller, not larger. Some may only multiply one coordinate instead of both coordinates. Others may confuse the original point with the image point when filling in the table. Teachers can help by having students trace from each original point to its matching image point before writing answers.
Implementation Guidance
This worksheet is a strong practice page after students have seen a few dilation examples. In class, it can be used for guided practice, small-group help, or a quick skill check. At home, a parent can ask the student to point to the old shape and the new shape before solving. That keeps the activity grounded in the picture, which is often easier for students than starting with numbers alone.
Details and Features
The worksheet includes multiple coordinate grids, labeled figures, and answer spaces for original and image points. It gives students repeated practice with both enlargements and reductions. The printable layout supports pencil-and-paper graph work without needing extra materials. It also includes reminder boxes to help students remember the scale factor rule.