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Right triangle LMN has vertices [tex]\( L(7, -3), M(7, -8) \)[/tex], and [tex]\( N(10, -8) \)[/tex]. The triangle is translated on the coordinate plane so the coordinates of [tex]\( L' \)[/tex] are [tex]\( (-1, 8) \)[/tex].

Which rule was used to translate the image?

A. [tex]\( (x, y) \rightarrow (x+6, y-5) \)[/tex]
B. [tex]\( (x, y) \rightarrow (x-6, y+5) \)[/tex]
C. [tex]\( (x, y) \rightarrow (x+8, y-11) \)[/tex]
D. [tex]\( (x, y) \rightarrow (x-8, y+11) \)[/tex]



Answer :

GinnyAnswer
To determine the rule used to translate the image of triangle [tex]\( LMN \)[/tex], we need to find the translation vector that moves point [tex]\( L(7, -3) \)[/tex] to point [tex]\( L'(-1, 8) \)[/tex].

Let's break this down step-by-step:

1. Identify the initial and final coordinates:
- Initial coordinates of point [tex]\( L \)[/tex]: [tex]\( (7, -3) \)[/tex]
- Final coordinates of point [tex]\( L' \)[/tex]: [tex]\( (-1, 8) \)[/tex]

2. Calculate the translation vector (dx, dy):
- [tex]\( dx \)[/tex] (change in x-coordinate) = final x - initial x
[tex]\[ dx = -1 - 7 = -8 \][/tex]
- [tex]\( dy \)[/tex] (change in y-coordinate) = final y - initial y
[tex]\[ dy = 8 - (-3) = 8 + 3 = 11 \][/tex]

3. Determine the translation rule based on the translation vector:
- The translation vector [tex]\((dx, dy)\)[/tex] is [tex]\((-8, 11)\)[/tex].
- This vector indicates the rule [tex]\((x, y) \rightarrow (x - 8, y + 11)\)[/tex].

Therefore, the correct translation rule that was used is:
[tex]\[ (x, y) \rightarrow (x - 8, y + 11) \][/tex]

Thus, the correct answer is:
(x, y) → (x - 8, y + 11).

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