Question

Polygon ABCD is drawn with vertices A(−4, −4), B(−4, −6), C(−1, −6), D(−1, −4). Determine the image coordinates of C′ if the preimage is reflected across y = 4.

C′(−3, 6)

C′(−3, 14)

C′(−1, 6)

C′(−1, 14)

Answer 1

(d) C'(-1, 14)

Explanation:

You want the coordinates of C' after the point C(-1, -6) is reflected across the line y = 4.

Reflection

Reflection across the horizontal line y=4 will not change the x-coordinate of the point, so C' has an x-coordinate of -1.

The point (-1, 4) on the line of reflection will be the midpoint of C and C', so we have ...

(C +C')/2 = (-1, 4)

C +C' = 2(-1, 4) = (-2, 8) . . . . .multiply by 2

C' = (-2, 8) -C

C' = (-2, 8) -(-1, -6) = (-1, 8+6)

C' = (-1, 14)

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Additional comment

Effectively, the reflection across the line y=4 is the transformation ...

(x, y) ⇒ (x, 8 -y)