Questions: What is the coordinate notation for a translation 3 units right and 5 units down? A. (x, y) -> (x+5, y-3) B. (x, y) -> (x-3, y+5) C. (x, y) -> (x-5, y+3) D. (x, y) -> (x+3, y-5)

What is the coordinate notation for a translation 3 units right and 5 units down? A. (x, y) -> (x+5, y-3) B. (x, y) -> (x-3, y+5) C. (x, y) -> (x-5, y+3) D. (x, y) -> (x+3, y-5)
Transcript text: What is the coordinate notation for a translation 3 units right and 5 units down? A. $(x, y) \rightarrow(x+5, y-3)$ B. $(x, y) \rightarrow(x-3, y+5)$ C. $(x, y) \rightarrow(x-5, y+3)$ D. $(x, y) \rightarrow(x+3, y-5)$
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Solution

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Solution Steps

To find the coordinate notation for a translation 3 units right and 5 units down, we need to adjust the x-coordinate by adding 3 and the y-coordinate by subtracting 5. This will give us the correct transformation for the given translation.

Step 1: Understand the Translation

To translate a point \( (x, y) \) by 3 units to the right and 5 units down, we adjust the coordinates as follows:

  • The x-coordinate is increased by 3: \( x' = x + 3 \)
  • The y-coordinate is decreased by 5: \( y' = y - 5 \)
Step 2: Apply the Translation to the Origin

Applying this translation to the origin point \( (0, 0) \):

  • New x-coordinate: \( 0 + 3 = 3 \)
  • New y-coordinate: \( 0 - 5 = -5 \)

Thus, the translated point is \( (3, -5) \).

Step 3: Identify the Correct Coordinate Notation

The coordinate notation for this translation is \( (x, y) \rightarrow (x+3, y-5) \).

Final Answer

\(\boxed{(x, y) \rightarrow (x+3, y-5)}\)

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