Two rectangles $ABCD$ABCD and $A'B'C'D'$A′B′C′D′ are plotted on a Coordinate Plane. In rectangle $ABCD$ABCD, $AB$AB is the left side, $CD$CD is the right side, $BC$BC is the top side, and $AD$AD is the bottom side. In rectangle $A'B'C'D'$A′B′C′D′, $A'$A′ is the left side, $C'$C′ is the right side, $B'$B′ is the top side, and $A'$A′ is the bottom side. The coordinates of the vertices of rectangle $ABCD$ABCD are $\left(-1,-2\right)$(−1,−2) for $A$A, $\left(-1,1\right)$(−1,1) for $B$B, $\left(2,1\right)$(2,1) for $C$C, and $\left(2,-2\right)$(2,−2) for $D$D. The coordinates of the vertices of rectangle $A'B'C'D'$A′B′C′D′ are $\left(-2,-4\right)$(−2,−4) for $A'$A′, $\left(-2,2\right)$(−2,2) for $B'$B′, $\left(4,2\right)$(4,2) for $C'$C′, and $\left(4,-4\right)$(4,−4) for $D'$D′. The coordinates of the vertices are not explicitly labeled on the graph.

Are the two rectangles similar, congruent or neither?

Congruent

Similar

Neither

What is the transformation from rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?

Rotation

Translation

Dilation

Reflection

What is the scale factor of the dilation from rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?

Easy

< 1min

Consider the triangle with vertices at $A$A$\left(-3,-2\right)$(−3,−2), $B$B$\left(2,1\right)$(2,1) and $C$C$\left(3,-3\right)$(3,−3), and the triangle with vertices at $A'$A′$\left(-9,-6\right)$(−9,−6), $B'$B′$\left(6,3\right)$(6,3) and $C'$C′$\left(9,-9\right)$(9,−9).

Easy

< 1min

Consider the quadrilateral with vertices at $A$A$\left(-3,-3\right)$(−3,−3), $B$B$\left(-3,3\right)$(−3,3), $C$C$\left(3,3\right)$(3,3) and $D$D$\left(3,-3\right)$(3,−3), and the quadrilateral with vertices at $A'$A′$\left(-9,-9\right)$(−9,−9), $B'$B′$\left(-9,9\right)$(−9,9), $C'$C′$\left(9,9\right)$(9,9) and $D'$D′$\left(9,-9\right)$(9,−9).

Easy

< 1min

Consider a transformation that causes one vertex of a triangle to move from $\left(x,y\right)$(x,y) to $\left(0.6x,0.6y\right)$(0.6x,0.6y).

Easy

< 1min

Outcomes

II.G.SRT.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

8.02 Similarity transformations

Interactive practice questions

Outcomes

II.G.SRT.2

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