What is the intersection of two planes? What about two lines?

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Presentation transcript:

What is the intersection of two planes? What about two lines? Warm Up Supplies Needed: Graphing Sheet, Dry Erase Marker, Eraser, Protractor What is the intersection of two planes? What about two lines?

TRANSFORMATIONS!!! https://www.youtube.com/watch?v=4TPgV7QFOcQ 4:13

Transformations A transformation is a function that changes the position, size, or shape of a figure.

Preimage and Image Pg. 801 The original figure is called the preimage. The resulting figure is called the image. A transformation maps the preimage to the image.

Transformations are Functions A function is a rule that pairs each input (x-value) with exactly one output (y-value).

Notation There are two types of notation that we use in transformations. Prime Notation Coordinate Notation

Pg. 801 You can use prime notation to name the image of a point. Note that a transformation is sometimes called a mapping.

Prime Notation Arrow notation () is used to describe a transformation, and primes (’) are used to label the image.

Pg. 801 Coordinate Notation: One way to write a rule for a transformation on a coordinate plane. The notation uses an arrow to show how the transformation changes the coordinates of a general point. i.e. (x, y)  (x + a, y + b).

pg. 801 A

You try!!! pg. 802 (B, C, 1 and 2)

Pg. 803 Rigid Motion: A transformation that changes the position of a figure without changing the size or shape of the figure. Two figures that have the same size and the same shape are called congruent! Translations, reflections, and rotations are rigid motions.

Try It Out! Graph these triangles on your graphing sheet. How can we prove they are congruent? Find the lengths of all of the sides. Find all of the angle measures

Pg. 805 Nonrigid Motions: Transformations that stretch or compress figures are not rigid motions because they do not preserve distance.

Dilations are Non-Rigid transformations (Scale factor = 2) (x, y)  (2x, 2y)

We are going to start learning about our first transformation!

What is a translation?

Translations First, read the article about how translations are used in Ohio State’s marching band.

Ohio State Marching Band https://www.youtube.com/watch?v=v3vp7H3eEfs Work on Translation WS with group!

pg. 808-813 (1-6, 10) For #5 and 6, just write the rule Homework pg. 808-813 (1-6, 10) For #5 and 6, just write the rule