For each transformation function F R2 R2 decide whether or

For each transformation function, F: R2   -> R2, decide whether or not it is an isometry of the Euclidean Plane. Then, classify the transformation.

2. For each transformation function, F: R R2, decide whether or not it is an isometry of the Euclidean plane (R2, dE). That is, decide whether it is distance- preserving (under Euclidean distance). Then, classify the transformation, if you can. x 6, y b, F(x, y) (2x, y)

Solution

An isometry is a transformation in which the original figure and its image are congruent.

(a) The function F(x, y) = (-x + 6, y) is an isometry. The transformation applied is a combination of translation and reflection. First, we apply reflection about y-axis on (x, y) to obtain (-x, y) then translate it 6 units along x-axis.

(b) The function F(x, y) = (-x + 6, y) is not an isometry in this case. Because, here we have a scaling by a factor of 2 along x-axis, and therefore, the dimensions of the object will change, consequently the original figure and its image are not congruent.