Question

Determine whether or not each sequence of transformations of trapezoid WXYZ results in trapezoid WXY'Z'. Select Yes if the sequence results in trapezoid WXYZ' and No if it does not

Answer 1

To solve this problem, we assign coordinates to WXYZ and W'X'Y'Z'.

Let the coordinates be:

• W(0,0), X(1,1), Y(3,1) and Z(4,0)

,

• W'(0,0), X'(-1,-1), Y'(-1,-3) and Z'(0,-4)

Next, we check each of the rules and see the ones that give us the coordinates of W'X'Y'Z'.

Option A

• Reflection over x-axis: W*(0,0), X*(1,-1), Y*(3,-1) and Z*(4,0)

,

• Rotation 90 degrees clockwise: W'(0,0), X'(-1,-1), Y'(-1,-3) and Z'(0,-4)

This gives the required coordinate,

Answer here is Yes.

Option B

• Reflection over y-axis: W*(0,0), X*(-1,1), Y*(-3,1) and Z*(-4,0)

,

• Rotation 90 degrees clockwise: W'(0,0), X'(1,1), Y'(1,3) and Z'(0,4)

This does not gives the required coordinate,

Answer here is No.

Option C

• Reflection over y-axis: W*(0,0), X*(-1,1), Y*(-3,1) and Z*(-4,0)

,

• Rotation 90 degrees counterclockwise: W'(0,0), X'(-1,-1), Y'(-1,-3) and Z'(0,-4)

This gives the required coordinate,

Answer here is Yes.

Option D

• Rotation 90 degrees clockwise: W*(0,0), X*(1,-1), Y*(1,-3) and Z*(0,-4)

,

• Reflection over x-axis: W'(0,0), X'(1,1), Y'(1,3) and Z'(0,4)

This does not gives the required coordinate,

Answer here is No.

Option E

• Rotation 90 degrees clockwise: W*(0,0), X*(1,-1), Y*(1,-3) and Z*(0,-4)

,

• Reflection over y-axis: W'(0,0), X'(-1,-1), Y'(-1,-3) and Z'(0,-4)

This gives the required coordinate,

Answer here is Yes.

Option F

• Rotation 90 degrees counterclockwise: W*(0,0), X*(-1,1), Y*(-1,3) and Z*(0,4)

,

• Rotation 180 degrees: W'(0,0), X'(1,-1), Y'(1,-3) and Z'(0,4)

This does not give the required coordinate,

Answer here is No.