Question

1. mp reason inductively a figure is translated by (x, y) → (x + 3, y − 4) then by (x, y) → (x − 3, y + 4). without graphing, how do you know the final position of the figure? write an argument that can be used to defend your solution.

Explanation:

Step1: Apply first translation to (x,y)

New coordinates: $(x + 3, y - 4)$

Step2: Apply second translation to result

New x: $(x + 3) - 3 = x$; New y: $(y - 4) + 4 = y$

Answer:

The final position is the original position of the figure. The two translations are inverse operations: the first adds 3 to x and subtracts 4 from y, and the second subtracts 3 from x and adds 4 to y, canceling each other out.