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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^{\prime}[/tex]?

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



Answer :

GinnyAnswer
To determine the \( y \)-value of the translated vertex \( P' \), we need to apply the given translation rule to the vertex \( P \).

The coordinates of vertex \( P \) are \( (-2, 6) \).

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

We apply this translation rule to the coordinates of \( P \):

1. For the \( x \)-coordinate of \( P \):
[tex]\[ x_P = -2 \][/tex]
Applying the translation rule:
[tex]\[ x' = x_P - 2 = -2 - 2 = -4 \][/tex]

2. For the \( y \)-coordinate of \( P \):
[tex]\[ y_P = 6 \][/tex]
Applying the translation rule:
[tex]\[ y' = y_P - 16 = 6 - 16 = -10 \][/tex]

Thus, the \( y \)-value of the translated vertex \( P' \) is \( -10 \). Therefore, the correct answer is:
[tex]\[ \boxed{-10} \][/tex]

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