In this Grade 7 lesson from Big Ideas Math Course 2 Accelerated (Chapter 11), students learn how to perform dilations in the coordinate plane by multiplying vertex coordinates by a scale factor to enlarge or reduce figures. Students identify dilations, compare similar figures produced by different scale factors, and explore how dilations relate to other transformations such as translations, reflections, and rotations. The lesson builds on students' understanding of coordinate plotting and integer multiplication to develop skills aligned with Common Core standards 8.G.3 and 8.G.4.
Section 1
Defining Dilations
A dilation is a transformation that changes the size of a figure by a scale factor with respect to a fixed point called the center of dilation.
All points on the original figure are mapped to corresponding points on the image such that the distance from the center to each image point is times the distance from the center to the corresponding original point.
Section 2
Defining the Scale Factor (k): Enlargements and Reductions
For a dilation with scale factor :
Section 3
Coordinate Rules for Dilations (Centered at Origin)
When performing a dilation on a coordinate grid where the Center of Dilation is the origin (0,0), the rule is the easiest of all transformations: simply multiply both the x and y coordinates of every vertex by the scale factor k.
Rule: (x, y) → (kx, ky)
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Section 1
Defining Dilations
A dilation is a transformation that changes the size of a figure by a scale factor with respect to a fixed point called the center of dilation.
All points on the original figure are mapped to corresponding points on the image such that the distance from the center to each image point is times the distance from the center to the corresponding original point.
Section 2
Defining the Scale Factor (k): Enlargements and Reductions
For a dilation with scale factor :
Section 3
Coordinate Rules for Dilations (Centered at Origin)
When performing a dilation on a coordinate grid where the Center of Dilation is the origin (0,0), the rule is the easiest of all transformations: simply multiply both the x and y coordinates of every vertex by the scale factor k.
Rule: (x, y) → (kx, ky)
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter