The point $A(-1,4)$ is translated five units right and three units down. Which rule describes the translation?

A. $(x, y) \rightarrow(x+5, y+3)$
B. $(x, y) \rightarrow(x+5, y-3)$
C. $(x, y) \rightarrow(x+3, y+5)$
D. $(x, y) \rightarrow(x-3, y+5)$

The translation rule for moving point A(-1, 4) five units to the right and three units down is given by the equation ( x , y ) → ( x + 5 , y − 3 ) . Hence, the correct answer is option B. This translation involves adding 5 to the x-coordinate and subtracting 3 from the y-coordinate.
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Answered by Anonymous | 2025-07-04

A translation of five units to the right corresponds to adding 5 to the x-coordinate.
A translation of three units down corresponds to subtracting 3 from the y-coordinate.
The translation rule is therefore ( x , y ) → ( x + 5 , y − 3 ) .
The correct answer is ( x , y ) → ( x + 5 , y − 3 ) .

Explanation

Analyze the problem Let's analyze the problem. We are given a point A ( − 1 , 4 ) and we need to find the translation rule after moving the point 5 units to the right and 3 units down.

Determine the translation rule Moving a point to the right means adding to its x-coordinate, and moving it down means subtracting from its y-coordinate. So, if we have a point ( x , y ) , translating it 5 units to the right and 3 units down results in the point ( x + 5 , y − 3 ) .

State the translation rule Therefore, the translation rule is ( x , y ) → ( x + 5 , y − 3 ) .


Examples
Imagine you're designing a video game. You want to move a character 5 steps to the right and 3 steps down on the screen. This translation rule helps you update the character's position by simply adding 5 to the x-coordinate and subtracting 3 from the y-coordinate, making the game development process easier.

Answered by GinnyAnswer | 2025-07-04