Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

[tex]$\overline{P L}$[/tex] has endpoints [tex]\(P(4,-6)\)[/tex] and [tex]\(L(-2,1)\)[/tex].

The segment is translated using the mapping [tex]\((x, y) \rightarrow (x+5, y)\)[/tex].

What are the coordinates of [tex]\(P'\)[/tex] and [tex]\(L'\)[/tex]?

A. [tex]\(P'(9,-6), L'(3,1)\)[/tex]
B. [tex]\(P'(4,-6), L'(3,1)\)[/tex]
C. [tex]\(P'(9,-6), L'(-2,1)\)[/tex]
D. [tex]\(P'(9,-1), L'(3,6)\)[/tex]

Sagot :

To determine the new coordinates of the endpoints of the segment [tex]$\overline{PL}$[/tex] after applying the translation, follow these steps:

1. Identify the given coordinates:
- Point [tex]\(P\)[/tex] has coordinates [tex]\((4, -6)\)[/tex].
- Point [tex]\(L\)[/tex] has coordinates [tex]\((-2, 1)\)[/tex].

2. Understand the translation mapping:
- The translation specifies that we should add 5 to the x-coordinate and keep the y-coordinate the same: [tex]\((x, y) \to (x + 5, y)\)[/tex].

3. Apply the translation to point [tex]\(P\)[/tex]:
- The x-coordinate of [tex]\(P\)[/tex] is 4. After applying the translation, the new x-coordinate will be [tex]\(4 + 5 = 9\)[/tex].
- The y-coordinate of [tex]\(P\)[/tex] is [tex]\(-6\)[/tex]. Since the y-coordinate doesn't change, it remains [tex]\(-6\)[/tex].
- Therefore, the new coordinates of [tex]\(P^{\prime}\)[/tex] are [tex]\((9, -6)\)[/tex].

4. Apply the translation to point [tex]\(L\)[/tex]:
- The x-coordinate of [tex]\(L\)[/tex] is [tex]\(-2\)[/tex]. After applying the translation, the new x-coordinate will be [tex]\(-2 + 5 = 3\)[/tex].
- The y-coordinate of [tex]\(L\)[/tex] is 1. Since the y-coordinate doesn't change, it remains 1.
- Therefore, the new coordinates of [tex]\(L^{\prime}\)[/tex] are [tex]\((3, 1)\)[/tex].

So, after applying the translation, the new coordinates of the endpoints are:
- [tex]\(P^{\prime}(9, -6)\)[/tex]
- [tex]\(L^{\prime}(3, 1)\)[/tex]

Therefore, the correct option is:
[tex]\[P^{\prime}(9, -6), L^{\prime}(3, 1)\][/tex]