Step 1
The given coordinates of triangle XYZ are
[tex]\begin{gathered} X=(-4,2) \\ Y=(-2,2) \\ Z=(-2,6) \end{gathered}[/tex]
The coordinates of the first transformation X'Y'Z' has coordinates
[tex]\begin{gathered} X^{\prime}=(-3,4) \\ Y^{\prime}=(-2,4) \\ Z^{\prime}=(-2,6) \end{gathered}[/tex]
Find the reason for the first transformation.
The first transformation is dilation and reduction
[tex]\begin{gathered} In\text{ triangle XYZ} \\ XY=\text{ 2units} \\ YZ=\text{ 4 units} \\ We\text{ can find XZ using Pythagoras theorem} \\ XZ=\sqrt[]{4^2+2^2} \\ XZ=\text{ }\sqrt[]{16_{}+4} \\ XZ=\sqrt[]{20} \\ XZ=2\sqrt[]{5}units \end{gathered}[/tex][tex]\begin{gathered} In\text{ triangle X'Y'Z'} \\ X^{\prime}Y^{\prime}=\text{ 1 unit} \\ Y^{\prime}Z^{\prime}=\text{ 2 units} \\ X^{\prime}Z^{\prime}\text{ = }\sqrt[]{1^2+2^2} \\ X^{\prime}Z^{\prime}=\sqrt[]{5}\text{ units} \end{gathered}[/tex]
Hence the dilation was by a scale factor of 1/2 which will bring about a reduction.
Step 2
Find the reasons for the second transformation
The second transformation is a reflection and the triangle X'Y'Z' is reflected over x=1
