Dilating Triangles Using Scale Factors
Dilating triangles using scale factors is a Grade 7 geometry skill in Big Ideas Math Advanced 2, Chapter 3: Angles and Triangles. A dilation multiplies all side lengths of a triangle by scale factor k while preserving all angle measures, resulting in a similar triangle. For example, dilating triangle ABC with vertices A(2,4), B(6,2), C(4,8) by k equals 2 about the origin gives A prime(4,8), B prime(12,4), C prime(8,16).
Key Concepts
A dilation transforms a triangle by multiplying all side lengths by a scale factor $k$, where $k 0$. If $k 1$, the triangle enlarges; if $0 < k < 1$, the triangle shrinks. The dilated triangle has vertices at positions that are $k$ times the distance from the center of dilation.
Common Questions
How do you dilate a triangle in the coordinate plane?
Multiply each vertex coordinate by the scale factor k. For a dilation from the origin with k equals 2, a point at (3, 5) maps to (6, 10). Apply this to each vertex of the triangle.
What happens to the side lengths and angles when a triangle is dilated?
Side lengths are multiplied by the scale factor k, making the triangle larger or smaller. Angle measures are preserved unchanged, so the dilated triangle is similar to the original.
What is the result of dilating a triangle by k equals 0.5?
Each side length is halved, making the image triangle half the size of the original. All angles remain the same, and the triangles are similar with a 2:1 ratio.
What textbook covers dilating triangles in Grade 7?
Big Ideas Math Advanced 2, Chapter 3: Angles and Triangles covers dilation transformations applied to triangles with various scale factors.