Dilations MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

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Presentation transcript:

Dilations MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

What is dilation?What is dilation? (click for video)

Dilation – an enlargement or reduction of a figure. The point at which the figure is either reduced or enlarged is called the center of dilation.

The dilation of a figure is always the product of the original and a scale factor. Scale factor – a positive number that is multiplied by the coordinates of the shape’s vertices.

How to enlarge a figure?How to enlarge a figure? (Click for video)

Let’s say you want to dilate ∆ABC by a scale factor of ¼, you need to multiply each coordinate of the original object by ¼. A (-4, -2): B (0, 5): C (4, -2): = A′ (-1, - ½) = B′ (0, 5 / 4 ) = C′ (1, - ½ ) x = -4 * ¼ = -1 y = -2 * ¼ = - ½ x = 0 * ¼ = 0 y = 5 * ¼ = 5 / 4 or 1 ¼ x = 4 * ¼ = 1 y = -2 * ¼ = - ½ Note: Since the scale factor is less than one, the dilated figure A′B′C′ is a reduction of the original triangle ABC.

On your own graph paper sketch the original and the dilated figures. A: (-3, 1) B: (-1, 4) C: (1, 4) D: (3, 1) Scale factor: 4 A′: (-12, 4) B′: (-4, 16) C′: (4, 16) D′: (12, 4) *This is an enlargement since the scale factor is greater than 1. Remember to multiply each coordinate by 4. C′C′ D′D′ B′B′ A′A′ AD CB

A′A′ C′C′ On your own graph paper sketch the original and the dilated figures. A: (-10, 0) B: (0, 10) C: (8, 5) Scale factor: 4 / 5 A′: (-8, 0) B′: (0, 8) C′: (6 2 / 5, 4) *This is a reduction since the scale factor is less than 1 but greater than 0. Remember to multiply each coordinate by 4 / 5. A B C B′B′

How do you find the scale factor when given the original coordinates and the image coordinates? What did you do to find the new image’s coordinates? So what will you have do to find the scale factor? Multiply the original by the scale factor. Divide the new image’s coordinates by the pre-image’s coordinates.

Find the scale factor of the following. A: (-2, 4)A′: (-1, 2) B: (8, 8)B′: (4, 4) C: (12, 0)C′: (6, 0) D: (2, -6)D′: (1, -3) Remember to divide the image’s coordinates by the originals’. √ Check the other vertices to make sure the scale factor works for each.