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'?
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.
