Question

Point A (1,2) is reflected around the line y=x and then translated by the rule (x,y)-> (x + 3, y - 7), and finally rotated 720 degrees. Find the x - coordinate of the FINAL image of Point A.

Answer 1

After reflecting Point A across the line y = x, translating by the rule (x + 3, y - 7), and rotating 720 degrees, the final x-coordinate of Point A is 5.

Step-by-step explanation:

The question involves several steps of transformations of a point on a coordinate plane: reflection, translation, and rotation. Starting with Point A (1,2), we reflect it across the line y = x resulting in Point A' (2,1). We then translate this point by the rule (x, y) -> (x + 3, y - 7), giving us Point A'' (5,-6).

Finally, we apply a 720-degree rotation. A full 360-degree rotation brings a point back to its original location, so a 720-degree rotation is equivalent to two full rotations, leaving the point unchanged from its position after the translation. Therefore, the x-coordinate of the final image of Point A is 5.