Question

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?

Answer 1

Answer: The new endpoints are (4,3) and (8,4)

Step by step:

First, reflext around the x axis. This really means flipping the sign of the y coordinates:

$(1,-3)\rightarrow(1,3)\\(5,-4)\rightarrow(5,4)$

Then apply horizontal translation by +3 units. A horizontal translation means adding units to the x coordinates:

$(1,3)\rightarrow(4,3)\\(5,4)\rightarrow(8,4)$