Curriculum Geometry B/ Algebra II
UNIT 1: TRANSFORMATIONS IN THE COORDINATE PLANE
EXPERIMENT WITH TRANSFORMATIONS IN THE PLANE |
|
MGSE9-12.G.CO.1 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.
MGSE9-12.G.CO.2 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).
MGSE9-12.G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MGSE9-12.G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MGSE9-12.G.CO.5 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.
MGSE9-12.G.CO.2 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).
MGSE9-12.G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MGSE9-12.G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MGSE9-12.G.CO.5 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.
KEY IDEAS
- A line segment is part of a line; it consists of two points and all points between them.
An angle is formed by two rays with a common endpoint.
A circle is the set of all points in a plane that are equidistant from a given point, called the center; the fixed distance is the radius.
Parallel lines are lines in the same plane that do not intersect.
Perpendicular lines are two lines that intersect to form right angles. - A transformation is an operation that maps, or moves, a pre-image onto an image.
A translation maps every two points P and Q to points P' and Q' so that PP' = QQ' and PP' is parallel to QQ'.
A reflection across a line m maps every point R to R' so that if R is not on m, then m is the perpendicular bisector of RR'; if R is on m, then R and R' are the same point.
A rotation of x° about a point Q maps every point S to S' so that SQ = S'Q; m∠SQS' = x°; pre-image point Q and image point Q' are the same. - A transformation in a coordinate plane can be described as a function that maps pre-image points (inputs) to image points (outputs). Translations, reflections, and rotations all preserve distance and angle measure because, for each of those transformations, the pre-image and image are congruent. But some types of transformations do not preserve distance and angle measure because the pre-image and image are not congruent.
- If vertices are not named, then there might be more than one transformation that will accomplish a specified mapping. If vertices are named, then they must be mapped in a way that corresponds to the order in which they are named.
|
|
RESOURCES |
|
|
|
|
|
|
|
|
|
translations_and_vectors.ppt | |
File Size: | 253 kb |
File Type: | ppt |