Question

In the figure shown, triangle RST undergoes reflections across two line. R''S''T’’ is the final image of RST

Answer 1

Answer: D.  y = -x

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Explanation:

Point T is at (-2,1)

When we reflect it over the line x = 0, aka the y axis, we use the rule $(x,y) \to (-x,y)$ so T(-2,1) becomes T ' (2, 1). The x coordinate flipped in sign, while the y coordinate stays the same.

Then the final transformation is reflecting over y = -x using the rule $(x,y) \to (-y, -x)$. Therefore, the point (2,1) moves to (-1, -2) which is where T'' is located in the diagram.

You apply the same two transformations for the points R and S to get R'' and S'' respectively.

Note: A composition of two reflections, where the lines of reflection aren't parallel, form a rotation. In this case, we have a 90 degree counterclockwise rotation when going from triangle RST to triangle R''S''T''.