8. bayangan titik A (X,Y) oleh dilatasi [0, 1/2] adalah A' (-2, 4). maka titik A= 9. bayangan titik B (8, -8) oleh dilatasi [p, -2], dengan P (7, -7) adalah B'

8) A(x, y) D[O, ½] A' (-2, 4)
uraikan
x' = kx
-2 = ½x
x = -2 × (2/1)
x = -4
y'= ky
4 = ½y
y = 4 × (2/1)
y = 8
titik A(-4, 8)

matriks
[tex] \binom{ {x}^{l} }{ {y}^{l} } = k \binom{x}{y} [/tex]
[tex] \binom{-2}{4} = \binom{1/2 \: \: \: \: \: \: \: \: \: 0}{0 \: \: \: \: \: \: \: \: \: 1/2} \binom{x}{y} \\ \binom{x}{y} = \frac{1}{1/4} \binom{1/2 \: \: \: \: \: \: \: \: \: \: \: 0}{0 \: \: \: \: \: \: \: \: 1/2} \binom{ - 2}{4} \\ \binom{x}{y} = 4 \binom{ -1}{ 2} \\ \binom{x}{y} = \binom{-4}{ 8} [/tex]
maka titik A (-4, 8)

9) B (8, -8) dilatasi [(7, -7), -2] B' (x', y')
x' = (x - p) k + p
x' = (8 - 7) (-2) + 7
x' = 1(-2) + 7
x' = -2 + 7
x' = 5
y' = (y - q) k + q
y' = (-8 + 7) (-2) + (-7)
y' = -(-2) - 7
y' = 2 - 7
y'= -5
B' (5, -5)

matriks
[tex] \binom{ {x}^{l} }{ {y}^{l} } = k \binom{x - p }{y - q} + \binom{p}{q} [/tex]

[tex] \binom{ x}{y} = \binom{ - 2 \: \: \: \: \: \: 0}{0 \: \: \: \: \: - 2} \binom{8 - 7}{ - 8 + 7} + \binom{7}{ - 7} \\ \binom{ {x}^{l} }{ {y}^{l} } = \binom{ - 2 \: \: \: \: \: \: \: 0}{0 \: \: \: \: \: - 2} \binom{1}{ - 1} + \binom{7}{ - 7} \\ \binom{ {x}^{l} }{ {y}^{l} } = \binom{ - 2 }{2} + \binom{7}{ - 7} \\ \binom{ {x}^{l} }{ {y}^{l} } = \binom{5}{ - 5} [/tex]

maka B' adalah (5, -5)