TRANSFORMATIONSBY: JESSICA RODRIGUEZ

TEKS FOR 8TH GRADE TRANSFORMATIONS

Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:

(A) generalize the properties of orientation and congruence of rotations, reflections, translations

(B) differentiate between transformations that preserve congruence

(C) explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate

plane using an algebraic representation [such as (x, y) → (x + 2, y + 2)]

TRANSFORMATION

Transformation is the use of translation, reflection, and a rotation of an image or set of points across a coordinate plane. The use of vertices to identify the exact method of transformation used for a given

problem.

EXAMPLE:

INTERACTIVE ACTIVITY FOR TRANSFORMATION

TRANSLATION

A point or set of points that are being moved to another location resulting in different coordinates without the changing of angle, area, line lengths, and shape. It is the same shape placed in a different location.

EXAMPLE:• Take the vertices of

∆LMN and use the algebraic equation to move the vertices to the left 5 units, and up 3 units. Resulting in the ∆L’M’N’.

INTERACTIVE ACTIVITY FOR TRANSLATION

REFLECTION

A congruence transformation that generates a mirror image of an object, without changing its size or shape. There are two three types of reflection across the x-axis, y-axis, and the line of y = x.

Examples of transformation geometry in the coordinate plane...

Reflection over x-axis: T(x, y) = (x, -y)

Reflection over y-axis: T(x, y) = (-x, y)

Reflection over line y = x: T(x, y) = (y, x)

EXAMPLE• The hexagon figure

ABCDEF is reflected across the mirror line on the x-axis at 2 (red line). Resulting in the reflected hexagon figure A’B’C’D’E’F’.

• The distance away from the mirror is the exact same on both sides.

INTERACTIVE ACTIVITY FOR REFLECTION

ROTATION

A rotation is a transformation that is performed by "spinning" an object or point around a fixed point known as the center of rotation. You can rotate your object at any degree measure, but 90°, 180°, and 270° are the most common. Rotations are done clockwise and counterclockwise.

EXAMPLE:

8/9/2015 4:14 PM - Screen Clipping

• The quadrilateral GHIJ is rotated along the fixed point O in a 90° clockwise rotation. Resulting in the quadrilateral image of G’H’I’J’

clockwise

INTERACTIVE ACTIVITY FOR ROTATION