How do i reflect triangle ABC if A (2,3), B (1,1), C(4,-3) over the x axis. Also rotating the triangle 90 degrees clockwise about the origin.

9514 1404 393

  see attached. red = reflected; blue = rotated

Step-by-step explanation:

The relevant coordinate transformations are ...

  (x, y) ⇒ (x, -y) . . . . . reflection over the x-axis

  (x, y) ⇒ (y, -x) . . . . . rotation 90° CW

In the attached figure, the red triangle A'B'C' is reflected. The blue triangle A"B"C" is rotated.

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Additional comment

Learning to visualize these transformations can take a little practice. It can help to draw the figure on a graph, trace it on another piece of paper or transparency, then move the copy to the new position relative to the old axes.

For reflection across the x-axis, the x-axis of the copy is aligned with the original, but the copy is flipped over so the old +y axis is aligned with the -y axis, and vice versa.

For rotation 90° CW, what was the +y axis becomes aligned with the +x axis, and what was the +x axis becomes aligned with the -y axis. That is, the figure is rotated 90° CW about the origin so anything in the first quadrant is moved to the 4th quadrant.

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step-by-step explanation: