Question
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\( 1 \leftarrow \) Given that the point \( (6,5) \) is on the graph of an equation that is symmetric with respect to the \( y \)-axis, what other point is on the graph? The point \( \square \) is also on the graph of the equation. (Type an ordered pair.)

Ask by Nguyen Davies. in the United States
Jan 31,2025

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Tutor-Verified Answer

Answer

The point \((-6, 5)\) is also on the graph.

Solution

When a graph is symmetric with respect to the \( y \)-axis, it means that for every point \( (x, y) \) on the graph, the point \( (-x, y) \) is also on the graph. Given the point \( (6, 5) \) is on the graph, its symmetric counterpart with respect to the \( y \)-axis is: \[ (-6, 5) \] **Answer:** \(\boxed{\,(-6,\ 5)\,}\)

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The Deep Dive

Since the equation is symmetric with respect to the \( y \)-axis, for every point \( (x, y) \) on the graph, the point \( (-x, y) \) must also be on the graph. Given the point \( (6, 5) \), the corresponding point due to this symmetry is \( (-6, 5) \). The point \( (-6, 5) \) is also on the graph of the equation.

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