Answer:
The coordinates of points P', Q' and R' are (-24, 32), (-64, 24) and (-8,-48), respectively.
Step-by-step explanation:
Vectorially speaking, the dilation of a vector with respect to a given point is defined by the following formula:
[tex]P'(x,y) = O(x,y) + r\cdot [P(x,y)-O(x,y)][/tex], [tex]r > 1[/tex] (1)
Where:
[tex]O(x,y)[/tex] - Point of reference.
[tex]P(x,y)[/tex] - Original point.
[tex]P'(x,y)[/tex] - Dilated point.
[tex]r[/tex] - Scale factor.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]P(x,y) = (-3, 4)[/tex], [tex]Q(x,y) = (-8,3)[/tex], [tex]R(x,y) = (-1,-6)[/tex] and [tex]r = 8[/tex], then the new coordinates of the triangle are, respectively:
[tex]P'(x,y) = (0,0) + 8\cdot [(-3,4)-(0,0)][/tex]
[tex]P'(x,y) = (-24, 32)[/tex]
[tex]Q'(x,y) = (0,0) + 8\cdot [(-8,3)-(0,0)][/tex]
[tex]Q'(x,y) = (-64, 24)[/tex]
[tex]R'(x,y) = (0,0) + 8\cdot [(-1,-6)-(0,0)][/tex]
[tex]R'(x,y) = (-8,-48)[/tex]
The coordinates of points P', Q' and R' are (-24, 32), (-64, 24) and (-8,-48), respectively.
