Topics
Congruence and Similarity
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New Zealand
Level 6 - NCEA Level 1

Transformations and Similarity

Lesson
Practice

Interactive practice questions

Consider the figures shown.

Loading Graph...
Two rectangles $ABCD$ABCD and $A'B'C'D'$A′B′C′D′ are plotted on a Cartesian 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.
a

Are the two rectangles similar, congruent or neither?

Congruent

A

Similar

B

Neither

C
b

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

Rotation

A

Translation

B

Dilation

C

Reflection

D
c

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
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Outcomes

GM6-5

Recognise when shapes are similar and use proportional reasoning to find an unknown length

GM6-8

Compare and apply single and multiple transformations

91031

Apply geometric reasoning in solving problems

91034

Apply transformation geometry in solving problems

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