Question

use coordinator notation to write the rule that maps each preimage to it's image then identify the transformation and confirm that it preserves length and angle measures

Answer 1

The rule that transform the preimage to the image can be represented below

$\begin{gathered} A(-4,4)\rightarrow A^{\prime}(4,4) \\ B(-1,2)\rightarrow B^{\prime}(2,1) \\ C(-4,1)\rightarrow C^{\prime}(1,4) \\ \\ The\text{ rule is express as} \\ (x,y)\rightarrow(y,-x) \end{gathered}$

The type of transformation is a rotation which is 270 degree.

Yes it preserves length and angles measured . Rotation is moving an object through a fixed point . so the length and angles are preserved.