options: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
problem_activity: Translate the line segment formed by the endpoints
$${E(0, 2)}$$
$${F (1,-4)}$$
according to the rule
$${(x,y) \rightarrow (x+5, y+4)}$$
.
Find the endpoints of the translated image algebraically.
Verify the translation on the coordinate plane.
Show the translation vector on the coordinate plane.


correct_option_index: 4