Question

Please help me with 7 and 9 I’m really confused and I really need help!!

Answer 1

Answer:

  7) K'(1, 1), N'(4, 0), Q'(4, 4)

  9) F'(4, 2), W'(4, 5), K'(3, 2)

Step-by-step explanation:

When you are not sure about reflections and rotations, it can be useful to actually draw a graph. The line of reflection is the perpendicular bisector of the segment connecting a point with its image. That is, the image is the same distance from the line on the other side. A point that is on the line of reflection is "invariant," it doesn't move.

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7) Reflecting across the x-axis changes the sign of the y-coordinate. That is all. Any point on the x-axis (y=0) is unchanged. The transformation is ...

  (x, y) ⇒ (x, -y)

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9) Reflecting across a vertical line changes the x-coordinate. The new value of x will be ...

  x' = 6 - x

The "6" is double the x-coordinate of the vertical line. The transformation is ...

  (x, y) ⇒ (6-x, y)

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Derivation of the formula for reflection on x=3

In general if M is the midpoint of a point (A) and its reflection (A'), then we have ...

  M = (A +A')/2

  2M = A + A'

  2M -A = A'

When a point is reflected across a vertical line, all of the y-coordinate values remain unchanged. So, for A=(x, y) and M=(3, y), we have ...

  A' = 2(3, y) -(x, y) = (6-x, 2y-y)

  A' = (6 -x, y)

So, the reflection transformation across the line x = 3 is ...

  (x, y) ⇒ (6-x, y)