Geometry Advanced Trasformations - 10 day full lessons includes lesson plans, worksheets, activities, smart notebook files, ppt, assessments, and answer key
I use Geometer's Sketchpad for this lesson
The student will be able to:
For a pair of points, both on a number line (1D) and the coordinate plane (2D), find a point that is a fractional distance between two points (, , etc.).
Given with A at the origin, then the point P which is of the way from A to B(x, y) is .
Given with A(c,d) not at the origin, then the point P which is of the way from A to B(x, y) is .
Use a similar triangle model to verify the transformation rule.
Point P is a dilation of B with center A.
Draw the reflection, translation, or rotation of a figure using a variety of methods (coordinate plane, patty paper, Geometer’s Sketchpad).
Translations
Concept of Rule: (x, y)®(x+h, y+k)
Verbal description: vertical/horizontal shifts
Reflections
Draw reflection over any line (NEW)
Recognize/draw the line of reflection between a figure and its image given the graph.
Concept of Rules
Across the x-axis: (x,y)®(x,-y)
Across the y-axis: (x,y)®(-x,y)
Across y = x: (x,y)®(y,x)
Dilations
Enlargement: (3x, 3y)
Reduction:
Dilation with center of dilation at the origin
Rotations (NEW)
Clockwise and counterclockwise
90°, 180°, 270°
Concept of Rules ( for multiples of 90)
Ex. 90°: (x,y) ®(-y,x)
Compare non-rigid, proportional transformations to non-rigid, non-proportional transformations
(x,y)®(2x,2y)
(x,y)®(2x,3y)
(x,y)®(2+x,2-y)
Determine and describe the relationship that exists between an image, its pre-image and the:
Line of reflection
Center of dilation
Center of rotation
Determine and describe the line of reflection of an image and a pre-image (on and off the coordinate grid).
Determine and describe the angle of rotation of an image and pre-image (on and off the coordinate grid)
Determine and describe the center of rotation of an image and pre-image (on and off the coordinate grid) when given 2 or more image points and their corresponding pre-image.
Determine and describe the center of dilation by finding the intersections of the lines passing through a point and its image (on and off the coordinate grid) when given at least two points in the image and pre-image
Determine the Image or Pre-image for a composition of transformations on a given two-dimensional figure.
Two or more rigid transformations
Two or more non-rigid transformations
A composition of both rigid and non-rigid
Include dilations where the center can be any point in the plane.