Geometry Unit 1: Transformations in the Coordinate Plane. Guided Notes

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Geometry Unit 1: Transformations in the Coordinate Plane Guided Notes

Standard: MGSE9 12.G.CO.1 Know precise definitions Essential Question: What are the undefined terms essential to any study of geometry? Transformation: The mapping, or movement, of all points of a figure in a plane according to a common operation, such as translation, reflection or rotation.

Standard: MGSE9 12.G.CO.1 Know precise definitions Essential Question: What are the undefined terms essential to any study of geometry? Pre image: A figure before a transformation has taken place.

Standard: MGSE9 12.G.CO.1 Know precise definitions Essential Question: What are the undefined terms essential to any study of geometry? Image: The result of a transformation.

Standard: MGSE9 12.G.CO.1 Know precise definitions Essential Question: What are the undefined terms essential to any study of geometry? Translation: A transformation that slides each point of a figure the same distance in the same direction.

Standard: MGSE9 12.G.CO.1 Know precise definitions Essential Question: What are the undefined terms essential to any study of geometry? Reflection: A transformation of a figure that creates a mirror image, flips, over a line.

Standard: MGSE9 12.G.CO.1 Know precise definitions Essential Question: What are the undefined terms essential to any study of geometry? Rotation: A transformation that turns a figure about a fixed point through a given angle and a given direction, such as 90 clockwise.

Standard: MGSE9 12.G.CO.1 Know precise definitions Essential Question: What are the undefined terms essential to any study of geometry? Isometry: a distance preserving map of a geometric figure to another location using a reflection, rotation or translation.

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we translate geometric figures in the coordinate plane? Translation: A transformation that slides each point of a figure the same distance in the same direction. Translations do not change the map of the figure! They are isometries! EX: Translate ΔABC 5 units down and 4 units left. (x, y) (x 4, y 5)

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we reflect geometric figures in a coordinate plane? Reflection: A transformation of a figure that creates a mirror image, flips, over a line. Reflections do not change the map of the figure! They are isometries! EX: Reflect the trapezoid about the x-axis. To reflect about the x-axis, (x, y) (x, -y).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we reflect geometric figures in a coordinate plane? EX: Reflect the trapezoid about the y-axis. To reflect about the y-axis, (x, y) (-x, y).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we reflect geometric figures in a coordinate plane? EX: Reflect the square about the line y = x. To reflect about y = x, (x, y) (y, x).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we reflect geometric figures in a coordinate plane? EX: Reflect the trapezoid about the line y = -x. To reflect about y= -x, (x, y) (-y, -x).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we reflect geometric figures in a coordinate plane? EX: Reflect the triangle about the line y = -3. To reflect about y = -3, (x, y) (x, 2(-3) y).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we reflect geometric figures in a coordinate plane? EX: Reflect the trapezoid about the line x = 6. To reflect about x = 6, (x, y) (2(6) x, y).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we identify the line of reflection in a coordinate plane? EX: What is the line of reflection in the figure?

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we rotate geometric figures in a coordinate plane? Rotation: A transformation that turns a figure about a fixed point through a given angle and a given direction Rotations do not change the map of the figure! They are isometries! EX: Rotate the trapezoid counterclockwise 90 about the origin. To rotate 90 counterclockwise about the origin, (x, y) (-y, x).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we rotate geometric figures in a coordinate plane? EX: Rotate the trapezoid clockwise 90 about the origin. To rotate 90 clockwise about the origin, (x, y) (y, -x).

EOC Example

Standard: 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). Essential Question: How do we rotate geometric figures in a coordinate plane? EX: Rotate the trapezoid 180 counterclockwise about the origin. To rotate 180 clockwise or counterclockwise about the origin, (x, y) (-x, -y).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we rotate geometric figures in a coordinate plane? EX: Rotate the trapezoid 270 counterclockwise about the origin. To rotate 270 counterclockwise about the origin, (x, y) (y, -x).

EOC Example

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we rotate geometric figures in a coordinate plane? EX: Rotate the trapezoid 270 clockwise about the origin. To rotate 270 clockwise about the origin, (x, y) (-y, x).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we rotate geometric figures in a coordinate plane about a given point? EX: Rotate the triangle 90 clockwise about the point (1, 1).

Standard: MGSE9 12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Essential Question: How do we transform geometric figures in a coordinate plane multiple times? EX: Rotate the triangle 90 clockwise, reflect the figure about the x-axis, then translate the figure 6 units to the left.

Standard: 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. Essential Question: How do we transform geometric figures in a coordinate plane multiple times? EX: Specify the sequence of transformations that will map ABCD to A B C D.

EOC Example

EOC Example

Standard: MGSE9 12.G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Essential Question: Which transformations carry figures onto themselves? EX: What transformation maps the regular hexagon to itself?

Standard: MGSE9 12.G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Essential Question: Which transformations carry figures onto themselves? EX: What transformations map the square onto itself?

EOC Example

EOC Example

EOC Example

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