If triangle ABC is dilated by a scale factor of m with the origin as the center of dilation to create triangle A'B'C', the coordinates of the dilated vertex B' are B' (9m, -8m).
In Mathematics and Euclidean Geometry, dilation is a type of transformation that is used for altering the dimensions of a geometric figure, but not its shape.
In this scenario and exercise, we would have to dilate the coordinates of the pre-image by using a scale factor of m centered at the origin as follows:
Ordered pair A (-3, 7) → (-3 × m, 7 × m) = Ordered pair A' (-3m, 7m).
Ordered pair B (9, -8) → (9 × m, -8 × m) = Ordered pair B' (9m, -8m).
Ordered pair C (-5, -6) → (5 × m, -6 × m) = Ordered pair C' (-5m, -6m).
In conclusion, we can logically deduce that the coordinates of the dilated vertex B' are (9m, -8m) when triangle ABC is dilated by a scale factor of m centered at the origin (0, 0).