Answer:
The coordinates of the dillated vertices are [tex]A'(x,y) = (2,2)[/tex], [tex]B'(x,y) = (4,4)[/tex], [tex]C'(x,y) = (8,2)[/tex] and [tex]D'(x,y) = (4,-2)[/tex].
Step-by-step explanation:
From Linear Algebra, we define dilation by the following equation:
[tex]P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation, dimensionless.
[tex]P(x,y)[/tex] - Original point, dimensionless.
[tex]k[/tex] - Scale factor, dimensionless.
[tex]P'(x,y)[/tex] - Dilated point, dimensionless.
If we know that [tex]O(x,y) = (0, 0)[/tex], [tex]k = 2[/tex], [tex]A(x,y) = (1,1)[/tex], [tex]B(x,y) = (2,2)[/tex], [tex]C(x,y) = (4,1)[/tex] and [tex]D(x,y) = (2,-1)[/tex], then the dilated points are, respectively:
Point A
[tex]A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)][/tex] (2)
[tex]A'(x,y) = (0,0) + 2\cdot [(1,1)-(0,0)][/tex]
[tex]A'(x,y) = (2,2)[/tex]
Point B
[tex]B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)][/tex] (3)
[tex]B'(x,y) = (0,0) + 2\cdot [(2,2)-(0,0)][/tex]
[tex]B'(x,y) = (4,4)[/tex]
Point C
[tex]C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)][/tex]
[tex]C'(x,y) = (0,0) + 2\cdot [(4,1)-(0,0)][/tex]
[tex]C'(x,y) = (8,2)[/tex]
Point D
[tex]D'(x,y) = O(x,y) + k\cdot [D(x,y)-O(x,y)][/tex]
[tex]D'(x,y) = (0,0) + 2\cdot [(2,-1)-(0,0)][/tex]
[tex]D'(x,y) = (4,-2)[/tex]
The coordinates of the dillated vertices are [tex]A'(x,y) = (2,2)[/tex], [tex]B'(x,y) = (4,4)[/tex], [tex]C'(x,y) = (8,2)[/tex] and [tex]D'(x,y) = (4,-2)[/tex].
