Sullivan Pearson
02/21/2024 · Junior High School

points) Given the mapping rule ( \( x, y) \rightarrow(x-6.5, y+3.2) \) and pre-image point \( (2,9) \), what is the ima pordinate after the mapping rule is applied? Show all your work.

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Step-by-step Solution

To find the image point after applying the mapping rule \( (x, y) \rightarrow (x - 6.5, y + 3.2) \) to the pre-image point \( (2, 9) \), we will follow these steps: 1. Identify the pre-image point coordinates: - \( x = 2 \) - \( y = 9 \) 2. Apply the mapping rule to the \( x \) coordinate: \[ x' = x - 6.5 = 2 - 6.5 = -4.5 \] 3. Apply the mapping rule to the \( y \) coordinate: \[ y' = y + 3.2 = 9 + 3.2 = 12.2 \] 4. Combine the transformed coordinates to find the image point: \[ (x', y') = (-4.5, 12.2) \] Thus, the image point after applying the mapping rule is \( \boxed{(-4.5, 12.2)} \).

Quick Answer

The image point is \((-4.5, 12.2)\).
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