Question

Graph XY with endpoints X(5,−2) and Y(3,−3) and its image after a reflection in the x-axis and then a rotation of 270 degrees about the origin.
What are the coordinates for XY after a reflection in the x-axis and then a rotation of 270 degrees about the orgin?

Please show all the work on how you got your answer.

Answer 1

Answer:

  X''(2, -5), Y''(3, -3)

Step-by-step explanation:

You know that reflection in the x-axis changes the sign of the y-coordinate. Points that used to be above the axis are now below by the same amount, and vice versa.

Rotation counterclockwise by 270° is the same as clockwise rotation by 90°. That maps the coordinates like this:

  (x, y) ⇒ (y, -x)

The two transformations together give you ...

  (x, y) ⇒ (x, -y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection across y=-x.

Using this mapping, we have ...

  X(5, -2) ⇒ X''(2, -5)

  Y(3, -3) ⇒ Y''(3, -3) . . . . . . on the equivalent line of reflection, so invariant

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The attachment shows the original segment in red, the reflected segment in purple, and the rotated segment in blue. The equivalent line of reflection is shown as a dashed green line.