123.1 and 3.245.1 and 5.2

Contraction : 3/4, 1/5 . .......As a dilation with a scale factor of less than 1, . but greater than 0 is Contraction Scale factor of the dilation = Image/Pre-image The coordinates of the given triangle are A(0,0), B(0, -6), C(8,0) Here the image is placed in the opposite side of the center of dilation C and also with a 1800 rotation. The coordinates of the given triangle are (-4,1), (-3,-4), (-2,-2) Expansion : 1.25, 3 ; and -2 ............ As a dilation with a scale factor greater than 1 is Expansion. **( -2 is -ve expansion opposite direction of the center of dilation with 1800 rotation) Scale factor of the dilation= M’P’/ MP = 4/10 = 0.4 Scale factor k = 1/2, and center of dilation = (0,0) or origin. The coordinates of image after dilation of coordinates (x,y) becomes (kx,ky) So, after the dilation the coodrinates of the image will be : (0*1/2,0*1/2), (0*1/2, -6*1/2), (8*1/2,0*1/2) = (0,0), (0, -3), (4,0) So, the scale factor will be less than 0 and has a –ve sign. Thus the scale factor of the dilation = - (R’S’/RS) = - (12cm/3cm) = -4. Scale factor k = -2 and center of dilation (0,0) or origin. The coordinates of image after dilation of coordinates (x,y) becomes (kx,ky) After the dilation the coordinates of the image will be : (-4*-2, 1*-2), (-3*-2, -4*-2), (-2*-2, -2*-2) = (8, -2), (6,8), (4,4) *(It is case of negative expansion or negative dilation)

SOLUTION: Dilations

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