Question

carlos performed a transformation on trapezoid efgh to create efgh, as shown in the figure below: figure of coordinate grid with trapezoids efgh and efgh what transformation did carlos perform to create efgh? options: rotation of 270° clockwise about the origin; reflection across the x - axis; rotation of 90° clockwise about the origin; reflection across the line of symmetry of the figure

Explanation:

First, identify coordinates of original trapezoid EFGH: E(-7,-4), F(-4,-4), G(-3,-6), H(-8,-6). The transformed E'F'G'H' has coordinates E'(-7,4), F'(-4,4), G'(-3,6), H'(-8,6). For each point (x,y) in EFGH, the corresponding point in E'F'G'H' is (x,-y), which matches the rule for reflection across the x-axis. Other options do not fit: a 270° clockwise rotation would give (y,-x), a 90° clockwise rotation would give (y,-x), and the figure has no line of symmetry that would map it to the upper left quadrant in this way.

Answer:

Reflection across the x-axis