Final answer:
To determine if the transformation named t is an isometry, we need to check if the lengths of the sides and angles of the transformed triangle are the same as the original triangle. Use the given transformation equations to evaluate the lengths of the sides and compare them to determine if the transformation is an isometry.
Step-by-step explanation:
A transformation is an isometry if it preserves distances and angles. To determine if the transformation named t is an isometry, we need to check if the lengths of the sides and the measures of the angles of the transformed triangle x'y'z' are the same as the original triangle xyz. If they are, then the transformation is an isometry.
We can start by evaluating the lengths of the sides using the given transformation equations.
For example, to find the length of side xy, we can use the distance formula, which is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Applying the transformation equations, we get:
d' = sqrt((x'2 - x'1)^2 + (y'2 - y'1)^2)
By comparing the lengths of the sides of the original and transformed triangles, we can determine if the transformation is an isometry.