Transformations and Similarity
In Changing Shapes, we looked at how congruent shapes may be transformed in one or more ways on a number plane. We can also transform similar shapes. These similar shapes will be dilated by a scale factor (ie. enlarged or reduced by a certain ratio) in addition to the transformation. The video attached to the examples below explains this process.
Examples
Question 1
Consider the figures shown.
Are the two triangles congruent, similar or neither?
Congruent
ASimilar
BNeither
CWhat is the transformation from triangle $ABC$ABC to triangle $A'B'C'$A′B′C′?
Dilation
AReflection
BRotation
CTranslation
DWhat is the scale factor of the dilation from triangle $ABC$ABC to triangle $A'B'C'$A′B′C′?
Question 2
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).
Are the two rectangles similar, congruent or neither?
congruent
Asimilar
Bneither
CWhat is the transformation from rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?
dilation
Areflection
Brotation
Ctranslation
DWhat is the scale factor of the dilation of rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?
Question 3
The quadrilateral with vertices at $\left(9,9\right)$(9,9), $\left(0,9\right)$(0,9), $\left(0,0\right)$(0,0) and $\left(9,0\right)$(9,0) is rotated 90 degrees clockwise around the origin and dilated by a factor of 2 with the origin as the centre of dilation.
What are the new coordinates of the vertices of the quadrilateral?
Write all four coordinates on the same line, separated by commas.