Question

I will give the rest of the answer choices later . I just need a brief explanation with the answer

Answer 1

Step 1

The given coordinates of triangle XYZ are

`\begin{gathered} X=(-4,2) \\ Y=(-2,2) \\ Z=(-2,6) \end{gathered}`

The coordinates of the first transformation X'Y'Z' has coordinates

`\begin{gathered} X^(\prime)=(-3,4) \\ Y^(\prime)=(-2,4) \\ Z^(\prime)=(-2,6) \end{gathered}`

Find the reason for the first transformation.

The first transformation is dilation and reduction

`\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}`
`\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}`

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