Warm-Up 2. What type of symmetry does the figure to the right have? How do you know?

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Presentation transcript:

Warm-Up 2. What type of symmetry does the figure to the right have? How do you know?

Pre-image The original figure before undergoing a transformation.

Image The new, resulting figure after a transformation

Isometry A transformation in which the preimage and image are congruent.

Which of the following are isometric?

they preserve angle measures Isometries not only preserve lengths, but they preserve angle measures parallel lines, and betweenness of points

Parallelogram MATH is transformed to Parallelogram LOVE by a rotation Parallelogram MATH is transformed to Parallelogram LOVE by a rotation. What is the image of HT? M A E V L H T EV O

Find the value of each variable, given that the transformation is an isometry.

* Translations (Slide your image over) * image * preimage

* Reflections (Flip your image over) * preimage * image

* Rotations (Turn your image about a fixed point) * image * preimage

(Enlarge or Shrink your image) * Dilations (Enlarge or Shrink your image) * preimage * image

Translations

Every point of the shape must move: To translate a shape: Every point of the shape must move: The same distance In the same direction

Translations Adding/ subtracting to the x and y variables generates a TRANSLATION on the coordinate plane. Adding to the X variable moves the pre-image RIGHT (x + 3, y) Subtracting from the X variable moves the pre-image LEFT . (x-3, y) Adding to the Y variable moves the pre-image UP. (x, y+2) Subtracting from the Y variable moves the pre-image DOWN. (x, y-2)

Example 1: Identify what the rule does to the pre-image. ( x + 1, y - 1) = (x -1, y + 1) =

Example 2: Identify the rule for a translation of the figure below 6 units right and 3 units down.

Example 3: Translate the image ABC by (x – 8, y + 2), given that ABC has the coordinates A(-2, 4), B (0, -8) and C (-3,5)

Practice!

Dilations

Dilations A Dilation is the ENLARGING or SHRINKING of a shape.

Dilation Notation Dk (x, y) = (kx, ky)

Example 1: Dilate the figure ABC by (2x, 2y) given that A (-2,-2) B(1,-1) and C(0, 2). What are the new coordinates?

Independent Practice

Exit Ticket Given figure ABC with coordinates A(1,4) B(2, 6) and C(-3, 2) Translate the figure using the rule T3,-2 (x+3, y – 2) Dilate the figure using the rule D1/3 or (1/3x, 1/3y)