PLEASE HELP 10 POINTS AND ILL MARK YOU BRAINLIEST Preston says the sequence of transformations that maps triangle ABC onto triangle DEF is: rotate 180 degrees about the origin, and then translate it up 7 units.

Chanel says the sequence of transformations that maps triangle ABC onto triangle DEF is: reflect it across the x axis then reflect it across the y axis and then translate it up 6 units and left 1 unit.

Part A
First take a look at Prestons sequence. How does a 180 degree 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 triangle ABC, and the coordinates of the rotated image, Triangle A’B’C’.

(x, y) ( , )

A( , ) A’( , )

B( , ) B’( , )

C( , ) C’( , )

Part C
How does a translation 7 units up change the coordinates of a shape?

Part D
Complete the table to find the rule for the translation, the coordinates of triangle A’B’C’ and the coordinates of the translated image, triangle A”B”C”.

(x, y) ( , )

A’( , ) A”( , )

B’( , ) B”( , )

C’( , ) C”( , )

Part E
Now look at Chanel’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 triangle ABC, and the coordinates of the reflected image, triangle A’B’C’.

(x, y) ( , )

A( , ) A’( , )

B( , ) B’( , )

C( , ) C’( , )

Part G
How does a reflection across the y axis change the coordinates of a shape?

Part H
Complete the table to find the rule for the reflection, the coordinates of triangle A’B’C’ and the coordinates of the reflected image, triangle A”B”C”.

(x, y) ( , )

A’( , ) A”( , )

B’( , ) B”( , )

C’( , ) C”( , )

Part I
How does a translation 6 units up and 1 unit left change the coordinates of a shape?

Part J
Complete the table to find the rule for the translation, the coordinates of triangle A”B”C” and the coordinates of the translated image, triangle A’’’B’’’C”’.

(x, y) ( , )

A”( , ) A’’’( , )

B”( , ) B’’’( , )

C”( , ) C’’’( , )

Part K
Who’s sequence proves triangle ABC is congruent to triangle DEF? Why?