To determine the coordinates of the translated triangle [tex]\( P'Q'R' \)[/tex] from the given translation rule [tex]\((x, y) \rightarrow (x+4, y-6)\)[/tex], follow these step-by-step instructions:
1. Starting Coordinates:
- The original coordinates of the triangle [tex]\(PQR\)[/tex] are:
[tex]\[
P(-8, 3), \quad Q(-8, 6), \quad R(-3, 6)
\][/tex]
2. Translation Rule:
- According to the translation rule [tex]\((x, y) \rightarrow (x+4, y-6)\)[/tex]:
3. Translating Each Point:
- For point [tex]\(P(-8, 3)\)[/tex]:
[tex]\[
x + 4 = -8 + 4 = -4
\][/tex]
[tex]\[
y - 6 = 3 - 6 = -3
\][/tex]
Therefore, the coordinates of [tex]\(P'\)[/tex] are:
[tex]\[
P'(-4, -3)
\][/tex]
- For point [tex]\(Q(-8, 6)\)[/tex]:
[tex]\[
x + 4 = -8 + 4 = -4
\][/tex]
[tex]\[
y - 6 = 6 - 6 = 0
\][/tex]
Therefore, the coordinates of [tex]\(Q'\)[/tex] are:
[tex]\[
Q'(-4, 0)
\][/tex]
- For point [tex]\(R(-3, 6)\)[/tex]:
[tex]\[
x + 4 = -3 + 4 = 1
\][/tex]
[tex]\[
y - 6 = 6 - 6 = 0
\][/tex]
Therefore, the coordinates of [tex]\(R'\)[/tex] are:
[tex]\[
R'(1, 0)
\][/tex]
4. Conclusion:
- The translated coordinates of triangle [tex]\(P'Q'R'\)[/tex] are:
[tex]\[
P'(-4, -3), \quad Q'(-4, 0), \quad R'(1, 0)
\][/tex]
From the choices provided, the coordinates [tex]\((-4, -3), (-4, 0), (1, 0)\)[/tex] correspond to the triangle [tex]\(P'Q'R'\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{P'(-4, -3), Q'(-4, 0), R'(1, 0)}
\][/tex]
