Question

1. what is the sequence of transformations for the image given? a reflect over the x - axis, translate (x + 8,y) b translate down 4 (y - 4) and to the right 5 (x + 5) c reflect over the y - axis then (x + 1,y + 1) d reflect over the x - axis then translate (x + 6,y)

Explanation:

Step1: Analyze option A

Reflection over x - axis changes (x,y) to (x, - y), then translation (x + 8,y) gives new point ((x + 8),-y).

Step2: Analyze option B

Translation down 4 and right 5 changes (x,y) to (x + 5,y - 4).

Step3: Analyze option C

Reflection over y - axis changes (x,y) to (-x,y), then translation (x+1,y + 1) gives (-x + 1,y + 1).

Step4: Analyze option D

Reflection over x - axis changes (x,y) to (x, - y), then translation (x+6,y) gives (x + 6,-y).

We need to visually check the given figure's transformation. But if we assume a general point (x,y) on the original figure:
For reflection over the y - axis, the rule is (x,y)→(-x,y). Then for a translation of (x + 1,y + 1), the new point is (-x+1,y + 1).

Answer:

C. Reflect over the y - axis then (x + 1,y + 1)