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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 :

GinnyAnswer
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]
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