Answered

IDNLearn.com: Where curiosity meets clarity and questions find their answers. Our platform provides prompt, accurate answers from experts ready to assist you with any question you may have.

Triangle [tex]$PQR$[/tex] has vertices [tex]$P(-2, 6)$[/tex], [tex]$Q(-8, 4)$[/tex], and [tex]$R(1, -2)$[/tex]. It is translated according to the rule [tex]$(x, y) \rightarrow (x-2, y-16)$[/tex].

What is the [tex]$y$[/tex]-value of [tex]$P'$[/tex]?

A. [tex]$-18$[/tex]
B. [tex]$-16$[/tex]
C. [tex]$-12$[/tex]
D. [tex]$-10$[/tex]

Sagot :

GinnyAnsweridn
To find the new coordinates of point [tex]\( P \)[/tex] after the translation, follow these steps:

1. Identify the original coordinates of point [tex]\( P \)[/tex]:
[tex]\[ P = (-2, 6) \][/tex]

2. Determine the rule for translation:
The translation rule is given by [tex]\( (x, y) \rightarrow (x - 2, y - 16) \)[/tex].

3. Apply the translation rule to the y-coordinate of [tex]\( P \)[/tex]:
Starting with the y-coordinate of [tex]\( P \)[/tex]:
[tex]\[ y = 6 \][/tex]
We need to translate this y-coordinate according to the rule:
[tex]\[ y' = y - 16 \][/tex]
Substituting the original y-coordinate:
[tex]\[ y' = 6 - 16 \][/tex]

4. Perform the subtraction:
[tex]\[ y' = -10 \][/tex]

Thus, the y-value of [tex]\( P' \)[/tex] after the translation is [tex]\( -10 \)[/tex].

So, the correct answer is:
[tex]\[ \boxed{-10} \][/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.