# Question #57dc3

Jan 4, 2017

$\left(x , y\right) \to \left(x + 3 , y - 4\right)$ translates
$\left(x , y\right) \to \left(- x , - y\right)$ rotates

#### Explanation:

If two figures are congruent in the plane, then they can be superposed exactly by a set of translations and rotations. The transformations

$\left(x , y\right) \to \left(3 x , 3 y\right)$ expands
$\left(x , y\right) \to \left(0.4 x , 0.4 y\right)$ shrinks

and the transformations

$\left(x , y\right) \to \left(x + 3 , y - 4\right)$ translates
$\left(x , y\right) \to \left(- x , - y\right)$ rotates

so those two last transformations generate congruent equivalents.