LESSON 84Dilations

VOCABULARY REVIEWTransformation – a change in position, size, or shape of a figurePreimage – the original figure in the transformationImage – the shape that is the result of the transformationIsometry – a transformation that does not change the size or shape of the figure

DILATIONS VOCABULARYDilation is a transformation that changes the size of a figure but not its shapeNot IsometryImage and Preimage are similar, but not congruent

DILATIONS VOCABULARY CONTINUEDReduction or Contraction – a dilation that results in a smaller figureEnlargement or Expansion – a dilation that results in a larger figureScale factor – the multiplier used in a dilationCenter of dilation – the intersection of lines that connect each corresponding point of the image and preimage The dilation to the right is a reduction, scale factor ½ and center is point E

DILATION OF A SEGMENT

Apply a dilation to using C as a center and a scale factor of 3.

DILATION OF A SEGMENT

Apply a dilation to using C as a center and a scale factor of 3.

DILATION OF A SEGMENT

Apply a dilation to using C as a center and a scale factor of ½.

DILATION OF A SEGMENT

Apply a dilation to using C as a center and a scale factor of ½.

DILATION OF A TRIANGLEGraph the triangle and its image after a dilation centered at the origin and a scale factor of ½

Write the transformation mapping

DILATION OF A TRIANGLEGraph the triangle and its image after a dilation centered at the origin and a scale factor of ½

Write the transformation mapping

APPLYING DILATION TO REAL LIFE EXAMPLESSuppose you want to enlarge a map that is 12 inches by 18 inches. If you choose the 120% enlargement setting on the scanner:

a) What will be the new lengths of the sides?

b) How will the perimeter of the original compare to the new?

c) How will the area of the original compare to the new?

APPLYING DILATION TO REAL LIFE EXAMPLESSuppose you want to enlarge a map that is 12 inches by 18 inches. If you choose the 120% enlargement setting on the scanner:

a) What will be the new lengths of the sides?

120% = 1.2 scale factor12(1.2) = 14.4 in18(1.2) = 21.6 in

APPLYING DILATION TO REAL LIFE EXAMPLESSuppose you want to enlarge a map that is 12 inches by 18 inches. If you choose the 120% enlargement setting on the scanner:

b) How will the perimeter of the original compare to the new?

120% = ? What do you think?This is a comparison of the new to the original. To answer the question we need the reciprocal.The original perimeter is of the new perimeter.

APPLYING DILATION TO REAL LIFE EXAMPLESSuppose you want to enlarge a map that is 12 inches by 18 inches. If you choose the 120% enlargement setting on the scanner:

c) How will the area of the original compare to the new?

is the ratio of the perimetersAny suggestions?Do we really have to find the areas?

REVIEW / QUESTIONSWhen a dilation is applied, it also affects the distance the image is from the centerPercent's are ratios Concentric circles can be looked at as a dilation