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 3 · 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.

$A coordinate grid showing triangle PQR near the origin and a larger triangle STU shifted up and to the right.$

Triangle $PQR$ has vertices $P(1, 0)$ , $Q(3, 0)$ , $R(1, 2)$ . Triangle $STU$ has vertices $S(5, 3)$ , $T(9, 3)$ , $U(5, 7)$ , and the triangles are similar with scale factor $2$ . Which sequence maps $\triangle PQR$ onto $\triangle STU$ ?

Dilate by scale factor $2$ centered at the origin, then translate $3$ units right and $3$ units up.

Translate $3$ units right and $3$ units up only (no dilation).

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

Reflect across the y-axis, then dilate by scale factor $2$ .