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Right triangle LMN has vertices [tex]\(L(7,-3)\)[/tex], [tex]\(M(7,-8)\)[/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 triangle, let's first focus on the coordinates of point [tex]\( L \)[/tex]. The original coordinates of point [tex]\( L \)[/tex] are [tex]\( (7, -3) \)[/tex], and the new coordinates after translation, [tex]\( L' \)[/tex], are [tex]\( (-1, 8) \)[/tex].

To find the translation rule, we need to determine how much the [tex]\( x \)[/tex]-coordinate and the [tex]\( y \)[/tex]-coordinate have changed.

1. Calculate the change in the [tex]\( x \)[/tex]-coordinate:
[tex]\[ \Delta x = x' - x = -1 - 7 = -8 \][/tex]

2. Calculate the change in the [tex]\( y \)[/tex]-coordinate:
[tex]\[ \Delta y = y' - y = 8 - (-3) = 8 + 3 = 11 \][/tex]

So, the translation changes each point [tex]\((x, y)\)[/tex] by [tex]\((x - 8)\)[/tex] and [tex]\((y + 11)\)[/tex].

Hence, the translation rule is:
[tex]\[ (x, y) \rightarrow (x - 8, y + 11) \][/tex]

The correct translation rule is:
[tex]\[ (x, y) \rightarrow (x - 8, y + 11) \][/tex]

Therefore, the correct option is:
[tex]\[ (x, y) \rightarrow (x - 8, y + 11) \][/tex]

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