Question

Triangle ABC is graphed on a coordinate plane with vertices at A (-3,7), B (9,-8), and

C(-5, -6). 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', what will be the coordinates of the dilated vertex
B?

Answer 1

Explanation:

Answer 2

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).