Transformation Rules

translation rule for a unit right and b units up

(x,y)-->(x + a, y + b) a= horizontal shift b = vertical shift

Translation rule for a units left and b units down

(x,y)——>(x-a,y-b)

reflection over the x-axis (Rule)

(x,y)-->(x, -y)

reflection over the y-axis (Rule)

(x,y)-->(-x, y)

Reflection over the y=x rule

(x,y) -> (y,x)

rotation of 90º Clockwise about the origin (Rule) same for 270 CCW

(x,y)-->(y, -x)

rotation of 180º CW/CCW about the origin (Rule)

(x,y)-->(-x, -y)

rotation of 90 CCW/270º Clockwise about the origin (Rule)

(x,y)-->(-y, x)

Reflection (Definition)

A transformation of a figure that FLIPS the figure across a line of symmetry

Translation (Definition)

A transformation of the movement (SLIDE) of a figure along a straight line

Rotation (Definition)

A transformation in which a figure is TURNED around a point of rotation

Identify the examples of rigid motions (congruent)

rotation, reflection, translation

The reflection of the point (4, 2) across the x-axis is the point ___.

(4, -2)

The reflection of the point (4, 2) across the y-axis is the point ___.

(-4, 2)

A reflection of the point (4,2) across the line y=x is the point_______

(2,4)

The translation of point (4, 2) using the vector

(1, 4)

The rotation of the point (4, 2) 90º Clockwise about the origin is the point ____________

(2, -4)

The rotation of the point (4, 2) 180º counterclockwise (CCW) about the origin is the point ____________

(-4, -2)

The rotation of the point (4, 2) 90º counter Clockwise (CCW) about the origin is the point ____________

(-2,4)

rotation of 90º Clockwise is the same rule as....

270 counter clockwise

rotation of 270º Clockwise is the same rules as...

90 counter clockwise

A line of reflection is the _________ _______________ of the any segment connecting a domain point to a range point.

perpendicular bisector

The magnitude (or degree) of rotation symmetry that maps a regular polygon onto itself formula

360/number of sides

order of rotational symmetry

the number of times the figure coincides with itself as it rotates through 360 degrees. For regular polygons it equals the number of sides.

Rigid figures preserve......

distance between points, angles measures, betweenness of points, and collinearity