Coordinate Plane: Reflections and Translations

A translation is a transformation that “slides” every point of a figure that same distance and in the same direction.

The figure and its translation are congruent and have the same orientation.

Translation Notation Description: move horizontally (right or left) a units and vertically (up or down) b units.

Mapping: (x,y) (x + a, y + b)

Symbol: T(a,b)

ExampleTranslate △ABC right 4 units.A(-2,1) B(1,0) C(-2,-2)

A(-2, 1)

B(1, 0)

C(-2, -2) C’(2, -2)

B’(5, 0)

A’(2, 1)

ExampleTranslate △JKL left 2 units; up 6 units.J(1,-1) K(4,-2) L(3,-4)

J(1, -1)

K(4, -2)

L(3, -4) L’(1, 2)

K’(2, 4)

J’(-1, 5)

A reflection is a transformation that “flips” a figure over a line called a line of reflection.

A figure and its reflection are congruent, but they have different orientations.

Rules of ReflectionReflection over the x-axis:(x, y) (x, -y)

(-x, y) (x, y) Reflection over the y-axis:

Reflection over the line y=x:(x, y) (y, x)

Example Reflect △PQR over the x-axis.P(2,4) Q(1,1) R(-3,3)

P(2,4)

Q(1,1)

R(-3,3) R’ (-3,-3)

P’ (2, -4)

Q’ (1, -1)

Example Reflect △LMN over the line y = x.L(-2, 0) M(2, -1) N(-1, -3)

L(-2, 0)

M(2, -1)

N(-1, -3) N’ (-3,-1)

L’ (0, -2)

M’ (-1, 2)