Transformations in Geometry

Translations and Transformations

• After translating the point (−4, 2) by moving 2 units left and 2 units up, the new coordinates become (−6, 4).

Sequences of Transformations

• To map triangle △ABC to triangle △A′B′C′, apply a rotation of 90° counterclockwise followed by a translation of 2 units to the right.

Triangular Transformation Rules

• For the transformation rule (x, y) → (−x, y), the new coordinates from points (-3, 4), (-4, 7), and (-8, 2) are formed by flipping them over the y-axis.
• When applying the transformation (x, y) → (x−6, y−4), the vertices (-4, 6), (-2, 2), and (-6, 2) are shifted down and left, resulting in new coordinates (-4, 1), (0, -2), and (-3, -9).

Vertex Coordinates

• The vertices of triangle △ABC are A(−4, 6), B(−2, 2), and C(−6, 2).
• The transformed vertices of triangle △A′B′C′ are A′(2, 6), B′(0, 2), and C′(4, 2).
• Mapping through a reflection across the y-axis and a translation of 2 units left transitions triangle △ABC to △A′B′C′.