Answer:
The rule of dilation is [tex]P'(x,y) = 3\cdot P(x,y)[/tex].
The vertices of the dilated triangle are [tex]A'(x,y) = (-21, -18)[/tex], [tex]B'(x,y) = (-15,-10)[/tex] and [tex]C'(x,y) = (-3,-15)[/tex], respectively.
Step-by-step explanation:
From Linear Algebra, we define the dilation by the following definition:
[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]k[/tex] - Scale factor, dimensionless.
[tex]P(x,y)[/tex] - Original point, dimensionless.
[tex]P'(x,y)[/tex] - Dilated point, dimensionless.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]k = 3[/tex], [tex]A(x,y) = (-7,-6)[/tex], [tex]B(x,y) = (-5,-2)[/tex] and [tex]C(x,y) =(-1,-5)[/tex], then dilated points of triangle ABC are, respectively:
[tex]A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)][/tex] (2)
[tex]A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)][/tex]
[tex]A'(x,y) = (-21, -18)[/tex]
[tex]B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)][/tex] (3)
[tex]B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)][/tex]
[tex]B'(x,y) = (-15,-10)[/tex]
[tex]C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)][/tex] (4)
[tex]C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)][/tex]
[tex]C'(x,y) = (-3,-15)[/tex]
The rule of dilation is:
[tex]P'(x,y) = 3\cdot P(x,y)[/tex] (5)
The vertices of the dilated triangle are [tex]A'(x,y) = (-21, -18)[/tex], [tex]B'(x,y) = (-15,-10)[/tex] and [tex]C'(x,y) = (-3,-15)[/tex], respectively.
