Question

which figure represents the image of trapezoid lmnp after a reflection across the x - axis?
figure a
figure b
figure c
figure d

Explanation:

Step1: Understand reflection across x - axis

When a figure is reflected across the \(x\) - axis, the \(x\) - coordinates of its points remain the same, and the \(y\) - coordinates are multiplied by \(- 1\). That is, if a point \((x,y)\) is reflected across the \(x\) - axis, its image is \((x, - y)\).

Step2: Analyze the position of trapezoid LMNP and other figures

Trapezoid LMNP is in the first - quadrant (positive \(y\) values). After reflection across the \(x\) - axis, the image should be in the fourth - quadrant (positive \(x\) values and negative \(y\) values).

• Figure A: Is in the second - quadrant (negative \(x\) values).
• Figure B: Is in the second - quadrant (negative \(x\) values for most of its part in terms of the main body's position relative to the axes).
• Figure C: Is in the fourth - quadrant (positive \(x\) values and negative \(y\) values).
• Figure D: Is in the third - quadrant (negative \(x\) values).

Answer:

figure C