IDNLearn.com: Your trusted platform for finding precise and reliable answers. Our platform provides trustworthy answers to help you make informed decisions quickly and easily.

Square ABCD was translated using the rule [tex]\((x, y) \rightarrow (x-4, y+15)\)[/tex] to form [tex]\(A' B' C' D'\)[/tex]. What are the coordinates of point [tex]\(D\)[/tex] in the pre-image if the coordinates of point [tex]\(D'\)[/tex] in the image are [tex]\((9, -8)\)[/tex]?

A. [tex]\((13, -23)\)[/tex]
B. [tex]\((5, 7)\)[/tex]
C. [tex]\((18, 1)\)[/tex]
D. [tex]\((-6, -4)\)[/tex]


Sagot :

To find the coordinates of point [tex]\( D \)[/tex] (the pre-image) given the coordinates of [tex]\( D' \)[/tex] (the image) and the translation rule, we need to reverse the translation process.

The given translation rule is:
[tex]\[ (x, y) \rightarrow (x-4, y+15) \][/tex]

Given the coordinates of [tex]\( D' \)[/tex] as [tex]\((9, -8)\)[/tex], we need to apply the reverse of the translation rule to find the original coordinates [tex]\( D \)[/tex].

The translation rule tells us how to move from [tex]\( D \)[/tex] to [tex]\( D' \)[/tex]:

[tex]\[ x' = x - 4 \][/tex]
[tex]\[ y' = y + 15 \][/tex]

To find the original coordinates [tex]\( (x, y) \)[/tex] from [tex]\( (x', y') \)[/tex], we solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] given the coordinates of [tex]\( D' \)[/tex]:

1. For the x-coordinate:
[tex]\[ x' = x - 4 \][/tex]
[tex]\[ 9 = x - 4 \][/tex]
[tex]\[ x = 9 + 4 \][/tex]
[tex]\[ x = 13 \][/tex]

2. For the y-coordinate:
[tex]\[ y' = y + 15 \][/tex]
[tex]\[ -8 = y + 15 \][/tex]
[tex]\[ y = -8 - 15 \][/tex]
[tex]\[ y = -23 \][/tex]

So, the coordinates of point [tex]\( D \)[/tex] are:
[tex]\[ (13, -23) \][/tex]

Hence, the correct coordinates of point [tex]\( D \)[/tex] in the pre-image are [tex]\( \boxed{(13, -23)} \)[/tex].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.