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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

Practice Test

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Exercise 8 Page 96

When a point with coordinates (x,y) is rotated 90^(∘) clockwise about the origin, the coordinates of its image are (y,- x).

A'(5,- 2), B'(2,- 1), C'(1,- 3)

A rotation is a transformation about a fixed point called center of rotation. Each point of the original figure and its image are the same distance from the center of rotation. When a clockwise rotation is performed about the origin, the coordinates of the image can be written in relation to the coordinates of the preimage.

Rotations About the Origin
90^(∘) Rotation	180^(∘) Rotation	270^(∘) Rotation
ccc Preimage & & Image [0.5em] (x,y) & → & (y,- x)	ccc Preimage & & Image [0.5em] (x,y) & → & (- x,- y)	ccc Preimage & & Image [0.5em] (x,y) & → & (- y,x)

We want to rotate a triangle 90^(∘) clockwise about the origin. Therefore, we can use the information in the above table to find the coordinates of the image of each vertex. ccc Preimage & & Image (x,y) & → & (y,- x) [0.5em] A(2,5) & & A'(5,- 2) [0.5em] B(1,2) & & B'(2,- 1) [0.5em] C(3,1) & & C'(1,- 3) We can now plot the obtained points and draw the image of the given triangle after the rotation!

preimage and image

Extra

Visualizing the Rotation

Let's rotate △ ABC 90^(∘) clockwise about the origin so that we can see how it is mapped onto △ A'B'C'.

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