Question

due date: friday 9.19.2025 must show your work. no work = no credit. write as ordered pair for each of the items (1,2) (2,3) (4,4) 8.g.2 which of these sequences of transformations would not return a shape to its original position? translate 3 units up, then 3 units down. reflect over line p, then reflect over line p again translate 1 unit to the right, then 4 units to the left, then 3 units to the right. rotate 120 counterclockwise around center c, then 220 rotate counterclockwise around c again. day 9.16.2025 must show your work. no work = no credit. (7.g.4) find the area of the shaded region 28

Explanation:

Step1: Analyze option A

Translating 3 units up and then 3 units down is the inverse - operation. If the original position of a point is \(y\), after translating 3 units up, the position is \(y + 3\), and after translating 3 units down, it is \((y + 3)-3=y\). So, it returns the shape to its original position.

Step2: Analyze option B

Reflecting a shape over a line \(p\) and then reflecting it over the same line \(p\) again is the inverse - operation. The first reflection changes the position of the shape with respect to the line \(p\), and the second reflection over the same line undoes the first transformation, returning the shape to its original position.

Step3: Analyze option C

Let the original \(x\) - coordinate of a point be \(x\). Translating 1 unit to the right gives \(x + 1\), then translating 4 units to the left gives \((x + 1)-4=x - 3\), and then translating 3 units to the right gives \((x - 3)+3=x\). So, it returns the shape to its original position.

Step4: Analyze option D

Rotating a shape 120° counter - clockwise around center \(C\) and then rotating 220° counter - clockwise around center \(C\) gives a total rotation of \(120^{\circ}+220^{\circ}=340^{\circ}
eq360^{\circ}\). A non - 360° rotation around a point does not return the shape to its original position.

Answer:

D. Rotate 120° counterclockwise around center C, then 220° rotate counterclockwise around C again.