Question

the figure in quadrant 3 (abcde) is congruent to the figure in quadrant 1 (abcde). what transformation took the first figure (pre - image) to the second figure? translation 9 units right and 2 units down reflection over the y - axis rotation 180 degrees counterclockwise around the origin rotation 90 degrees clockwise around the origin

Explanation:

Step1: Analyze translation

Translation changes position but not orientation. Comparing pre - image and image, orientation is not just shifted, so it's not a translation.

Step2: Analyze reflection over y - axis

For a reflection over the y - axis, (x,y)→(-x,y). The pre - image and image do not match this transformation rule.

Step3: Analyze 180 - degree rotation

For a 180 - degree counter - clockwise rotation around the origin, (x,y)→(-x,-y). This does not match the transformation from pre - image to image.

Step4: Analyze 90 - degree clockwise rotation

For a 90 - degree clockwise rotation around the origin, (x,y)→(y, - x). If we take a point in the pre - image in quadrant 3, say A(-3,5), after 90 - degree clockwise rotation around the origin, it becomes A'(5,3) which is consistent with the position of A' in quadrant 1.

Answer:

Rotation 90 degrees clockwise around the origin