100 points and !

chanel says the sequence of transformations that maps trapezoid pqrs onto trapezoid klmn is: rotate it 90 degrees counterclockwise, and then dilate it by a scale factor of 1/2.

preston says the sequence of transformations that maps trapezoid pqrs onto trapezoid klmn is: reflect it across the x-axis, and then dilate it by a scale factor of 1/2.

part a
start with chanel’s sequence. how does a 90-degree counterclockwise rotation about the origin change the coordinates of a shape?

part b
complete the table to find the rule for the rotation, the coordinates of trapezoid pqrs, and the coordinates of the rotated image, trapezoid p′q′r′s′.
original coordinates new coordinates
(x, y) ( , )
p( , ) p′( , )
q( , ) q′( , )
r( , ) r′( , )
s( , ) s′( , )

part c
how does a dilation by a scale factor of 1/2 change the coordinates of a shape?

part d
complete the table to find the rule for the dilation, the coordinates of trapezoid p′q′r′s′, and the coordinates of the dilated image, trapezoid p″q″r″s″.
original coordinates new coordinates
(x, y) ( , )
p′( , ) p″( , )
q′( , ) q″( , )
r′( , ) r″( , )
s′( , ) s″( , )
part e
now, look at preston’s sequence. how does a reflection across the x-axis change the coordinates of a shape?

part f
complete the table to find the rule for the reflection, the coordinates of trapezoid pqrs, and the coordinates of the reflected image, trapezoid p′q′r′s′.
original coordinates new coordinates
(x, y) ( , )
p( , ) p′( , )
q( , ) q′( , )
r( , ) r′( , )
s( , ) s′( , )

part g
how does a dilation by a scale factor of 1/2 change the coordinates of a shape?

part h
complete the table to find the rule for the dilation, the coordinates of trapezoid p′q′r′s′, and the coordinates of the dilated image, trapezoid p″q″r″s″.
original coordinates new coordinates
(x, y) ( , )
p′( , ) p″( , )
q′( , ) q″( , )
r′( , ) r″( , )
s′( , ) s″( , )

part i
whose sequence proves trapezoid pqrs is similar to trapezoid klmn? why?