Back to Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, and dilations — Problem 4 · Task Set 24

Exercises: Understand Similarity Through Sequences of Transformations

Work through each section in order. A dilation centered at the origin with scale factor $k$ maps $(x, y)$ to $(kx, ky)$. The scale factor is the ratio of corresponding side lengths. Show your work where indicated.

Grade 8·21 problems·~35 min·Common Core Math - Grade 8·container·8-g-a-4

Work through problems with immediate feedback

Fluency Practice

Find scale factors, check proportionality, and describe transformation sequences. Show your work.

$A coordinate grid showing triangle ABC in the first quadrant and a larger triangle DEF in the third quadrant.$

Triangle $ABC$ has vertices $A(0, 0)$ , $B(2, 0)$ , $C(0, 3)$ . Triangle $DEF$ has vertices $D(0, 0)$ , $E(-4, 0)$ , $F(0, -6)$ , and the triangles are similar with scale factor $2$ . Which sequence maps $\triangle ABC$ onto $\triangle DEF$ ?

Dilate by scale factor $2$ centered at the origin, then rotate $180\degree$ about the origin.

Dilate by scale factor $2$ centered at the origin only (no rotation).

Rotate $180\degree$ about the origin only (no dilation).

Translate down and left only.