Compositions Transformations

What is the image of (x,y) after the composition of transformations defined by R_-90 o r_y=x?

• (-x,y)

• (-y,x)

• (x,-y)

• (-y,-x)

What is the image of (x,y) under r_{x-axis o} R ₉₀ ?

• (-y,x)

• (x,-y)

• (y,-x)

• (-y,-x)

What are the coordinates of point A' , the image of point A(-4, 1) after the composite transformation R₉₀ o r_y=x where the origin is the center of rotation?

• (-1, -4)

• (-4, -1)

• (1, 4)

• (4, 1)

The coordinates of triangle JRB  are ,J(1, -2) , R(-3, 6) and B(4, 5) .  What are the coordinates of the vertices of its image after the transformation T_{2, -1} o r_y-axis ?

• (3, 1), (-1, -7), (6, -6)
• (3, -3), (-1, 5), (6, 4)
• (1, -3), (5, 5), (-2, 4)
• (-1, -2), (3, 6), (-4, 5)

If the coordinates of point P are (x,y) , then R₉₀ o R₁₈₀ is

• (-y,x)

• (-x,-y)

• (-y,-x)

• (y,-x)

What is the algebraic rule for the composition R₂₇₀ o T_-2,5?

• (-y-5, x-2)

• (y+5, -x-2)

• (y+5, -x+2)

• (y-2, -x+5)

Chose the correct transformation:
(x, y) ----- (x, -y)

• Reflection across x-axis
• Reflection across y-axis
• 90 degree clockwise rotation
• 90 degree counter clockwise rotation

What is the algebraic rule for the composition T_-1,1 o R₁₈₀?

• (-x+1, -y-1)

• (-x-1, -y+1)

• (-x-1, -y-1)

• (x-1, y+1)

What does the parallel lines theorem state?

• Reflections across two parallel lines is the same as a single rotation.

• Reflections across two parallel lines is the same as a single translation.

• Reflections across two parallel lines is the same as a single reflection.

• Reflections across two parallel lines is the same as two translations.

What is the rule for the following reflection? 

• Reflection across      x-axis
• Reflection across        y-axis
• Reflection across            y = x
• Reflection across          y = −x