Task# Effects of Dilations on Length, Area, and Angles

Illustrative MathematicsVaries

The purpose of this task is for students to study the impact of dilations on different measurements: segment lengths, area, and angle measure. When a triangle is dilated by scale factor s>0, the base and height change by the scale factor s while the area changes by a factor of s^2: as seen in the examples presented here, this is true regardless of the center of dilation. While they scale distances between points, dilations do not change angles. While x and y coordinates have not been given to the vertices of the triangle, the coordinate grid serves the same purpose for the given centers of dilation.