Composite Rigid Transformations

Which sequence of rigid motions will prove ABC ≅ RST?

• a line reflection over y = x

• a rotation of 180 around (1,0)

• reflection over the x-axis followed by a translation 6 units right

• reflection over x-axis followed by a reflection over y = 1

Identify which sequence of transformations could map pentagon ABCDE onto pentagon A”B”C”D”E”, as shown below.

• dilation followed by rotation

• translation followed by rotation

• reflection followed by translation

• reflection followed by another reflection

Triangle XYZ has vertices X(-2, 2) Y(3, 2) and Z(-5, -6). Rotate the figure 180 degrees, translate it 2 units up and 4 units right, then dilate by a scale factor of 2. What are the new coordinates?

• X'''(8,4) Y'''(-2,4) Z'''(14,20)

• X'''(12,0) Y'''(2,0) Z'''(18,16)

• X'''(12,0) Y'''(2,0) Z'''(3, 4)

• X'''(8,4) Y'''(2,0) Z'''(14,20)

Which of the following describes the sequence of transformations shown?

• Reflect across the x-axis and then rotate -90 degrees around the origin

• Rotate -90 degrees around the origin and then translate down.

• Reflect across the x-axis and then reflect across the y-axis.

• Translate up and then rotate 90 degrees about the origin.

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 T2, -1 o Ry-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)

What goes last in the composition?

R_D,90(r_y-axis(T_2,-3(triangle ABC)))

• Translation up 2, left 3

• Translation right 2, down 3

• Draw triangle ABC

• Rotate about point D 90 degrees

• Reflect over y-axis

Which would be the correct notation for the composition of transformations from blue to red to green?

• T<-4,0> ^o R_{y axis} 

• T<0,-4> ^o R_{y axis} 

•  R_{y axis} o T<0,-4> 

•  R_{x axis} o R_{y axis} 

What are the series of rigid motions that would map ∆ABC onto ∆A''B''C''?

• a reflection followed by a rotation

• a reflection followed by a translation

• a translation followed by a rotation

• a translation followed by a reflection

Find the image of A( -3, 5) after translating (x,y) --> (x-6 , y -1) then reflecting across the line x= -1

• ( 7, 4)

• ( 4, 7)

• (-5, 4)

• (4, -5)

Find the image of A( -3, 5) after translating (x,y) --> (x , y-4) then reflecting across the y-axis

• (3,1)

• (3, -1)

• (-1, 5)

• (-1, 3)