Questions: If P=(-2,7), Find: Ry-axis(P) ([?],[ ])

Transcript text: If $P=(-2,7)$, Find: $R_{y \text {-axis }}(P)$ $([?],[$ ] $)$

Solution

To find the reflection of a point $ P $ across the y-axis, we need to negate the x-coordinate of the point while keeping the y-coordinate the same.

Step 1: Identify the Given Point

We are given the point $ P = (-2, 7) $.

Step 2: Reflect the Point Across the y-axis

To find the reflection of the point $ P $ across the y-axis, we negate the x-coordinate while keeping the y-coordinate the same.

Mathematically, if $ P = (x, y) $, then the reflection $ R_{y \text{-axis}}(P) $ is given by: \[ R_{y \text{-axis}}(P) = (-x, y) \]

Step 3: Apply the Reflection Formula

For the given point $ P = (-2, 7) $: \[ R_{y \text{-axis}}(P) = (-(-2), 7) = (2, 7) \]

The reflection of the point $ P = (-2, 7) $ across the y-axis is: \[ \boxed{(2, 7)} \]

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