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Translate a point (x, y) 4 units left and 2 units down, and then 3 units right and 5 units up.
Mathematics
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Step-by-step solution
4 stepsTo translate a point by a certain amount horizontally and vertically, you add or subtract from its coordinates.
- Moving right means adding to the -coordinate.
- Moving left means subtracting from the -coordinate.
- Moving up means adding to the -coordinate.
- Moving down means subtracting from the -coordinate.
Since no initial coordinates for a shape are provided, we will express the translated coordinates in terms of an arbitrary original point .
- Translate 4 left and 2 down.
Identify the changes in coordinates.
Moving 4 left means $x \to x - 4$. Moving 2 down means $y \to y - 2$.Apply the changes to the original coordinates $(x, y)$.
The new coordinates $(x', y')$ will be $(x-4, y-2)$. The image coordinates are $\boxed{(x-4, y-2)}$.2. Translate 3 right and 5 up.
Identify the changes in coordinates.
Moving 3 right means $x \to x + 3$. Moving 5 up means $y \to y + 5$.Apply the changes to the original coordinates $(x, y)$.
The new coordinates $(x', y')$ will be $(x+3, y+5)$. The image coordinates are $\boxed{(x+3, y+5)}$.
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