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Triangle XYZ has coordinates X(2,4), Y(-3,4), and Z(-3,1). If the triangle is translated using the rule (x, y) → (x-2, y+1), what are the coordinates of Y'?

A. Y'(-5,5)
B. Y'(0,5)
C. Y'(-5,2)
D. Y'(-1,3)

Sagot :

GinnyAnswer
Let's analyze this translation problem step by step.

We have the original coordinates of point [tex]\( Y \)[/tex] as [tex]\( (-3, 4) \)[/tex].

The translation rule given is: [tex]\((x, y) \rightarrow (x - 2, y + 1)\)[/tex].

We need to apply this rule to the coordinates of point [tex]\( Y \)[/tex] to find its new location, [tex]\( Y' \)[/tex].

1. Start with the original coordinates:
[tex]\( x = -3 \)[/tex]
[tex]\( y = 4 \)[/tex]

2. Apply the translation rule:
- For the x-coordinate: [tex]\( x' = x - 2 = -3 - 2 \)[/tex]
- For the y-coordinate: [tex]\( y' = y + 1 = 4 + 1 \)[/tex]

3. Perform the calculations for each coordinate:
- [tex]\( x' = -3 - 2 = -5 \)[/tex]
- [tex]\( y' = 4 + 1 = 5 \)[/tex]

So, the new coordinates of [tex]\( Y' \)[/tex] after the translation are [tex]\( (-5, 5) \)[/tex].

Hence, the correct new coordinates of [tex]\( Y' \)[/tex] are:

[tex]\[ Y'(-5, 5) \][/tex]

Therefore, the correct option is:
[tex]\[ Y'(-5, 5) \][/tex]
This corresponds to option 1.
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