MODULE IV VOCABULARYPART I

MODULE IV

• Module IV more than any module thus far, will overlap with others.

• Module IV is called simply, “Triangles” and we have already intensively discussed these!

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• When I transform a figure it is important to discuss what is preserved.

• To say something is preserved in math is to say that it stays the same through a transformation.

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• The features that can be preserved are– Distance– Angle Measure– Orientation– Area

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• Distance is the measure of the length between points of a figure.

• Angle measure is the measure of the angles.

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• Orientation is the order the points of the figure fall in.

• For instance, the orientation of the figures below are not the same.

A

C

B

C’

B’

A’

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• Area refers to the size of the area.• What transformation have we done that

would NOT preserve area?• What transformations would preserve area?

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• Lastly today, we will discuss horizontal and vertical stretches.

• In doing so, we will examine how the area of such figures change.

MODULE IV• When I am horizontally stretching something,

I am essentially changing ONLY the x element by a given scale factor.

• When I am vertically stretching something, I am essentially changing ONLY the y element by a given scale factor.

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• So say I started with the figure below.

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• The coordinates that create this triangle are (2, 8), (4, 0) and (0, 0).

• If I am asked to horizontally stretch this figure, by a factor of 2.

MODULE IV• My points would now be (4, 8), (8, 0) and (0, 0)

MODULE IV• See? Each x value is multiplied

by the scale factor.• What if I was “stretching” my

figure by a scale factor of ½?• What if I was stretching my

figure vertically?

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• How do the area’s of these figures compare? • Well, that depends on how many dimensions

are changing and by how much.• Say we were dealing with our last stretch.

MODULE IV• The original triangle had a base of 4 and a

height of 8. • Therefore its area was 16 units².• The new triangle has a base of 8 and a height

of 8. • So it’s new area is 32.

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• The area is multiplied by each dimension’s scale factor.

• If there is a horizontal stretch of 2 and a vertical stretch of 4, the area change will be 8.

• Today, you’ll be asked to do all these things.