Line segment XY has endpoints at (1, −3) and (5, −4). The segment reflects over the x-axis. Then, it undergoes a translation 3 units to the right. What are the new coordinates for the endpoints? Does the transformation affect the length of the line?
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Coordinates are (4,3) and (8, 4). No, the length of the line segment does not change.
Step-by-step explanation:
On reflection of a line about the x axis, the x coordinates of its end points never change. However, the sign of the y coordinates is reversed. So, after reflection, the end points of the line segment become (1,3) and (5,4).
Now, on translating the segment to the right, the x coordinates increase by a value of 3, while the y coordinates remain the same. Hence, the new end points of the line segment are (4,3) and (8,4).
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