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The image of a point is given by the rule [tex]r_y=(-x, y) \rightarrow(-4,9)[/tex]. What are the coordinates of its pre-image?

A. [tex](-9,4)[/tex]
B. [tex](-4,-9)[/tex]
C. [tex](4,9)[/tex]
D. [tex](9,-4)[/tex]

Sagot :

GinnyAnswer
To determine the original coordinates of the point before the transformation, we need to understand the given transformation rule:

[tex]\[ r_y = -x(x, y) \rightarrow (-4, 9) \][/tex]

This rule implies a specific transformation applied to the coordinates [tex]\((x, y)\)[/tex]. Let's break it down:

1. The first part of the transformation, [tex]\( -x \)[/tex], suggests that the original x-coordinate of the point is negated in the transformed point.
2. The second part indicates that the original y-coordinate is preserved to become the x-coordinate in the transformed point.

Given the transformed coordinates [tex]\((-4, 9)\)[/tex]:

- The transformed x-coordinate is [tex]\(-4\)[/tex]. According to the rule, this means the original y-coordinate was [tex]\(-(-4) = 4\)[/tex].
- The transformed y-coordinate is [tex]\(9\)[/tex]. According to the rule, this means the original x-coordinate was [tex]\(9\)[/tex].

Therefore, reversing the transformation, the original coordinates of the point are [tex]\((9, 4)\)[/tex].

So, among the given options:
- [tex]\((-9, 4)\)[/tex]
- [tex]\((-4, -9)\)[/tex]
- [tex]\((4, 9)\)[/tex]
- [tex]\((9, -4)\)[/tex]

The correct pre-image of the point is:
[tex]\[ (9, 4) \][/tex]
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