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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remotecontrolbrain remotecontrolbrain · Answer 1 · 2018-11-20T19:59:05+01:00

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:

[tex](1,-3)\rightarrow(1,3)\\(5,-4)\rightarrow(5,4)\\[/tex]

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

[tex](1,3)\rightarrow(4,3)\\(5,4)\rightarrow(8,4)\\[/tex]

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alokdubeyvidyaatech alokdubeyvidyaatech · Answer 2 · 2021-11-14T18:31:16+01:00

Line segment XY has endpoints at (1, −3) and (5, −4).

The new coordinates for the endpoints is (4, 3) and (8, 4)

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

[tex](1,-3)[/tex] ⇒ [tex](1, 3)[/tex]

[tex](5,-4)[/tex] ⇒ [tex](5,4)[/tex]

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

[tex](1,3)[/tex] ⇒ [tex](4,3)[/tex]

[tex](5,4)[/tex]⇒ [tex](8,4)[/tex]

Therefore, the new coordinates for the endpoints is (4, 3) and (8, 4).

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