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Find the new set of coordinates given the scale factor for k > 1. E = (-1, -2), F = (2, -5), G = (5, -1), H = (1, 1) Scale factor = 6 E'= F' = G' = H' =

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Answer:

The new set of coordinates are
E'(x,y) = (-6,-12),
F'(x,y) = (12,-30),
G'(x,y) = (30,-6) and
H'(x,y) = (6,6).

Explanation:

Vectorially speaking, dilation can be defined by this equation:


D'(x,y) = O(x,y) +k\cdot (D(x,y)-O(x,y)) (1)

Where:


O(x,y) - Center of dilation.


D(x,y) - Original point.


k - Scale factor.


D'(x,y) - Dilated point.

Let suppose that center of dilation is located at origin, we determine the new set of coordinates below:


E'(x,y) = O(x,y) +k\cdot (E(x,y)-O(x,y))


E'(x,y) = (0,0) +6\cdot (-1,-2)


E'(x,y) = (-6,-12)


F'(x,y) = O(x,y) + k\cdot (F(x,y)-O(x,y))


F'(x,y) = (0,0) +6\cdot (2,-5)


F'(x,y) = (12,-30)


G'(x,y) = O(x,y) + k\cdot (G(x,y)-O(x,y))


G'(x,y) = (0,0) + 6\cdot (5,-1)


G'(x,y) = (30,-6)


H'(x,y) = O(x,y) +k\cdot (H(x,y)-O(x,y))


H'(x,y) = (0,0) + 6\cdot (1,1)


H'(x,y) = (6,6)

The new set of coordinates are
E'(x,y) = (-6,-12),
F'(x,y) = (12,-30),
G'(x,y) = (30,-6) and
H'(x,y) = (6,6).

User OttherCreek
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