Answer:
The new set of coordinates are [tex]E'(x,y) = (-6,-12)[/tex], [tex]F'(x,y) = (12,-30)[/tex], [tex]G'(x,y) = (30,-6)[/tex] and [tex]H'(x,y) = (6,6)[/tex].
Step-by-step explanation:
Vectorially speaking, dilation can be defined by this equation:
[tex]D'(x,y) = O(x,y) +k\cdot (D(x,y)-O(x,y))[/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation.
[tex]D(x,y)[/tex] - Original point.
[tex]k[/tex] - Scale factor.
[tex]D'(x,y)[/tex] - Dilated point.
Let suppose that center of dilation is located at origin, we determine the new set of coordinates below:
[tex]E'(x,y) = O(x,y) +k\cdot (E(x,y)-O(x,y))[/tex]
[tex]E'(x,y) = (0,0) +6\cdot (-1,-2)[/tex]
[tex]E'(x,y) = (-6,-12)[/tex]
[tex]F'(x,y) = O(x,y) + k\cdot (F(x,y)-O(x,y))[/tex]
[tex]F'(x,y) = (0,0) +6\cdot (2,-5)[/tex]
[tex]F'(x,y) = (12,-30)[/tex]
[tex]G'(x,y) = O(x,y) + k\cdot (G(x,y)-O(x,y))[/tex]
[tex]G'(x,y) = (0,0) + 6\cdot (5,-1)[/tex]
[tex]G'(x,y) = (30,-6)[/tex]
[tex]H'(x,y) = O(x,y) +k\cdot (H(x,y)-O(x,y))[/tex]
[tex]H'(x,y) = (0,0) + 6\cdot (1,1)[/tex]
[tex]H'(x,y) = (6,6)[/tex]
The new set of coordinates are [tex]E'(x,y) = (-6,-12)[/tex], [tex]F'(x,y) = (12,-30)[/tex], [tex]G'(x,y) = (30,-6)[/tex] and [tex]H'(x,y) = (6,6)[/tex].
