Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C'. Describe the transformation using words. Make sure you refer to the characteristics and the coordinates. Draw a line segment from point A to the reflecting line, and then draw a line segment from point A' to the reflecting line. What do you notice about the two line segments you drew? Do you think you would see the same characteristic if you drew the line segment connecting B with the reflecting line and then B' with the reflecting line? How do you know?
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When reflected over the x-axis, the x-coordinates of points A, B and C will remain the same. Only the y-coordinates will change and the change will be only in the sign of the y-coordinate. The magnitude of the y-coordinate will remain the same.
Part 2: The line segment AD is equal in length to the line segment A'D.
(The square in the middle just says AD is perpendicular to the x-axis and A'D is perpendicular to the x-axis. You don't have to draw them. It is just to illustrate the point that the line segment is drawn so it is perpendicular to the x-axis.)
Part 3: Yes, if line segments are drawn from points B and B' to the x-axis, they will form one straight line and the line segment BE will equal in length to the line segment B'E where E is the point where the line segment meets the x-axis.
"How do you know?"
A point with coordinates (a,b) when reflected about the x-axis becomes (a, -b). Therefore, the magnitude of the y-coordinate, |b| is the same for both points. Also, since the x-coordinate is the same for both points, a line segment drawn to the x-axis will meet at the same point and the two line segments will form one straight line.
From @aum I know but I don't understand what he means.
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part 1: ABC is flipped across the y axis and its points the same distance from the y axis
Part 2:The 2 line segments are the same length and connect to the y axis at the same location
Part 3: Yes because as the A and "A' B and B,' are the same distanse apart