Question

Which is the image of the point (9,-4) after a reflection about line y = 2 then translated along the vector <-2,4>?

A. (7,4)
B. (9,8)
C. (7,0)
D. (7,12)

Answer 1

Answer: Choice D. (7, 12)

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Step-by-step explanation:

Start at (9,-4). Move 6 units up to arrive at (9,2). This second point is on the horizontal mirror line of y = 2. We move another 6 units to get to (9,8).

Going from (9,-4) to (9,8) represents reflecting over the line y = 2.

Now apply the translation vector <-2,4> which says "shift to the left 2 units and shift up 4 units". That translation vector is the same as writing the rule
`(x,y) \to (x-2,y+4)`

Applying that translation to the point (9,8) moves us to (7,12)

Check out the diagram below.