Geometry Transformations

Reflection over the x-axis

• (x, y) --> (x, -y)

• (x, y) --> (-x, y)

• (x, y) --> (y, x)

• (x, y) --> (-y, -x)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Reflection over the y-axis

• (x, y) --> (x, -y)

• (x, y) --> (-x, y)

• (x, y) --> (y, x)

• (x, y) --> (-y, -x)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Reflection over the line y=x

• (x, y) --> (x, -y)

• (x, y) --> (-x, y)

• (x, y) --> (y, x)

• (x, y) --> (-y, -x)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Reflection over the line y = -x

• (x, y) --> (x, -y)

• (x, y) --> (-x, y)

• (x, y) --> (y, x)

• (x, y) --> (-y, -x)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

translation

• (x, y) --> (-y, x)

• (x, y) --> (-x, -y)

• (x, y) --> (y, -x)

• (x, y) --> (x +r/-l, y +u/- d)

• (x, y) --> (cx, cy)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

dilation from the origin

• (x, y) --> (-y, x)

• (x, y) --> (-x, -y)

• (x, y) --> (y, -x)

• (x, y) --> (x +/- h, y +/- h)

• (x, y) --> (cx, cy)

Tags

CCSS.8.G.A.3

rotation clockwise by 90 degrees

• (x, y) --> (-y, x)

• (x, y) --> (-x, -y)

• (x, y) --> (y, -x)

• (x, y) --> (x +/- h, y +/- h)

• (x, y) --> (cx, cy)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

rotation counter-clockwise by 270 degrees

• (x, y) --> (-y, x)

• (x, y) --> (-x, -y)

• (x, y) --> (y, -x)

• (x, y) --> (x +/- h, y +/- h)

• (x, y) --> (cx, cy)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

rotation clockwise or counter-clockwise by 180 degrees

• (x, y) --> (-y, x)

• (x, y) --> (-x, -y)

• (x, y) --> (y, -x)

• (x, y) --> (x +/- h, y +/- h)

• (x, y) --> (cx, cy)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

rotation counter-clockwise by 90 degrees

• (x, y) --> (-y, x)

• (x, y) --> (-x, -y)

• (x, y) --> (y, -x)

• (x, y) --> (x +/- h, y +/- h)

• (x, y) --> (cx, cy)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5