Wednesday, November 7, 2018 Warm-up Use the grid from yesterday s warm-up space to plot the pre-image ABCD and the points that are transformed by the rule (x, y) (2x, 2y) 5 2 2 5 2 4 0 0 Talk about quiz Dilations Objectives Content: I will compute and draw the coordinates of the image of a dilated figure in a coordinate plane. Social: I will work with the members of my group well. Language: I will clearly write my reasoning in my notes.
What do you notice that seems a little out of the ordinary? http://wikimedia.org
Word Real world example What does it mean in this context? Dilate Similar Scale Your doctor dilates your eyes during your annual physical. You and your friend have similar tastes in music. A map is a scale drawing of a city. Word Geometry example What does it mean in this context? Dilate Similar Scale A geometric figure is a dilation of another geometric figure. Dilation produces a polygon is similar to original polygon. Scale drawing in the coordinate plane.
Check Quiz
TRANSLATION ROTATION REFLECTION
Description Angle measures preserved? Parallelism preserved? Betweenness preserved? Distance (size) preserved? ISOMETRY? TRANSFORMATIONAL GEOMETRY Translations Reflections Rotations Slide Slide Flip Turn
TRANSLATION ROTATION same shape same size RIGID MOTION TRANSFORMATIONS REFLECTION Translations, Rotations, and Reflections are ISOMETRIES.
TRANSLATION ROTATION REFLECTION same shape DIFFERENT size DILATION
same shape DIFFERENT size DILATION Dilations are NOT Isometries.
Description TRANSFORMATIONAL GEOMETRY Translations Reflections Rotations Dilations Slide Slide Flip Turn Enlarge or Reduce Angle measures preserved? Parallelism preserved? Betweenness preserved? YES YES YES YES YES YES YES YES YES Distance (size) preserved? YES YES YES ISOMETRY? YES YES YES
Dilation is used to map an image that is similar to the original image (pre-image). The pre-image and image of a dilated polygon have: the same shape proportionate corresponding sides
Dilation is used to map an image that is similar to the original image (pre-image). Dilated polygons are SIMILAR.
Dilation is used to map an image that is similar to the original image (pre-image). Dilated polygons are SIMILAR. ABCD ~ A B C D
Translations, reflections, and rotations are congruence transformations. Congruence transformations are rigid motions. In rigid motions, the original image (pre-image) and the image are congruent. A dilation is a similarity transformation. A dilation is a transformation which produces an image that is the same shape as the pre-image a different size of the pre-image A similarity transformation is a rigid motion followed by a dilation. Dilations include the following components: scale factor, or ratio of dilation and the center of the dilation, a fixed point in the plane about which all points are contracted or expanded. Notation D k (x, y) = kx, ky where D is the center of dilation and k is the scale factor. The image created by a dilation is either an enlargement or a reduction.
Drawing a dilation in the coordinate plane. (x, y) (2x, 2y) 5 2 2 5 2 4 0 0 (x, y) ( 1 2 x, 1 2 y) 5 2 2 4 2 5 0 0 In this example we will dilate a figure by the scale factors of k = 1 2 and k = 2
Do the figures appear to be dilations?
Do the figures appear to be dilations?
Do the figures appear to be dilations?
Do the figures appear to be dilations?
Do the figures appear to be dilations?
Do the figures appear to be dilations?
Practice 4 4 0 4 (x, y) (4x, 4y) 8 8 4 0 (x, y) ( 1 4 x, 1 4 y) 4 4 0 4 8 8 4 0
PBL Work