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What is the y-coordinate of point D after a translation of [tex]\((x, y) \rightarrow (x + 6, y - 4)\)[/tex]?

[tex]\(D'(3.5, \square)\)[/tex]

Sagot :

GinnyAnsweridn
To find the new [tex]$y$[/tex]-coordinate of point [tex]\(D\)[/tex] after the translation, let's follow these steps:

1. Identify the original coordinates of point [tex]\(D\)[/tex]: The given coordinates of point [tex]\(D\)[/tex] are [tex]\( (3.5, y_D) \)[/tex].

2. Determine the translation vector: The translation vector given is [tex]\((x + 6, y - 4)\)[/tex]. This means we are adding 6 to the [tex]$x$[/tex]-coordinate and subtracting 4 from the [tex]$y$[/tex]-coordinate of point [tex]\(D\)[/tex].

3. Apply the translation to the [tex]$y$[/tex]-coordinate:
- The original [tex]$y$[/tex]-coordinate of point [tex]\(D\)[/tex] is [tex]\(y_D = 0\)[/tex].
- According to the translation vector, we need to subtract 4 from the [tex]$y$[/tex]-coordinate: [tex]\( y_D - 4 \)[/tex].

4. Calculate the new [tex]$y$[/tex]-coordinate:
- [tex]\( y_D - 4 = 0 - 4 = -4 \)[/tex].

Therefore, after applying the translation to point [tex]\(D\)[/tex], the new [tex]$y$[/tex]-coordinate of [tex]\(D'\)[/tex] is [tex]\(-4\)[/tex].

So, the translated point [tex]\(D'\)[/tex] will have coordinates [tex]\((3.5, -4)\)[/tex].
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