Download 9.7 Identify and Perform Dilations Center of dilation

9.7 Identify and Perform Dilations
Dilation- tÿ,j °ÿtÿ,,,tjifÿ!:(!W'ljt(!,ÿdl;!i,,,ÿ,t%!ÿ
Center of dilation-tlÿl
A dilation with center C and scale factor k is a
transformation that maps every point P in the plane to a
point P', so that the following properties are true:
1.) If P is not point C, then CP' is coincident to CP, and
CP' = k(CP), where k > 0 and k ÿ 1.
k:t,
2.) IfP is point C, then P = P'.
**The dilation is a
if 0 < k < 1 and it is an
if k> 1.
**In a dilation, every image is similar to its
preimage.
Coordinate notation for a dilation:
(x,y)-->(kx,ky)
Example 1 Find the scale factor of the dilation. Then tell
whether the dilation is a reduction or enlargement.
!0
15
Scalar Multiplication- ÿJTtl',Iÿ'i!ÿ
Example 2 The vertices of XYZW are (-4,4);
(2,8); (6,2); and (-2,-4). Use scalar
multiplication to find the image of XYZW after a
dilation with the center at the origin and a scale
factor of 2"
q ÿ
1
-- - q t -J.
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f
f
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Example 3 The vertices of ALMN are L(2,-3);
M(3,-1)and N(4,-2). Find the image of ALMN after a
translation (x,y)-,(x-3,y+2) and dilation centered at the
origin with scale factor 3o
ÿ'-- ÿ
iÿ,--O-ÿI,,ÿÿ !0,,)-. ÿ" (0,ÿ)
H(,-I,--;'-.) -ÿi'..lÿ (i,o) ÿk!'' (.7,o}
Example 4- Perform a dilation with a scale factor of 2
with the center of dilation at point C.