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# Dilations

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2 What really confuses me is just the center part, it messes up my calculations. Could someone help?

Jan 14, 2021

### 2+0 Answers

#1
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X = (-4,2)      Y  = (6,0)   Z  =   (-2, -4)

Center of Dilation    =  ( -2,-4)

Call (x , y)  the point to be dilated

Dilation rule =  ( x + 2, y + 4)

Apply the scale Factor  across this  =  ( 3x + 6, 3y+ 4)

Translate  Back  = (  3x + 6  - 2  ,  3y + 4 - 4)  = ( 3x +4, 3y  )

So    working backwards to calculate  A, B  and  C

3x  +  4  =  -4         3y =  2

3x  =  -8                   y = 2/3       So    A =   ( -8/3, 2/3)

x   = -8/3

And

3x +  4 =  6           3y =  0

3x  =  2                    y = 0        So    B =  (2/3, 0)

x = 2/3

And

3x + 4 = -2           3y  =  -4

3x  =  -6                 y =  -4/3     So   C  = ( -2, - 4/3)

x = -2   Jan 14, 2021
#2
+1

Center of Dilation   = A  =  (  -2, 3)

Call  (x , y)   the point to be dilated

Dilation Rule = ( x + 2, y - 3)

Apply Scale Factor over this  =   ( 4x + 8,  4y  - 12)

Translate  Back  = (  4x + 8 - 2 ,  4y - 12  + 3)  =  (   4x + 6, 4y - 9)

So applying this to C  to get C'  we have

(4(5) + 6 ,  4(-2) - 9 )  =  ( 26, -17)  =  C'   Jan 14, 2021