Question

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what is true about a point and its reflection across the y-axis? opposite x-coordinates; same y-coordinate same x-coordinate; opposite y-coordinates opposite x-coordinates; opposite y-coordinates same x-coordinate; same y-coordinate

Explanation:

To determine the relationship between a point and its reflection across the \( y \)-axis, we analyze the coordinates of the given points \( D(-4, -8) \) and its reflection \( C(4, -8) \).

• For the \( x \)-coordinates: The \( x \)-coordinate of \( D \) is \( -4 \) and of \( C \) is \( 4 \), which are opposites (since \( -4 = -1\times4 \)).
• For the \( y \)-coordinates: The \( y \)-coordinate of both \( D \) and \( C \) is \( -8 \), so they are the same.

This pattern holds for any point \((x, y)\) and its reflection across the \( y \)-axis, which is \((-x, y)\). So the correct description is "opposite \( x \)-coordinates; same \( y \)-coordinate".

Answer:

opposite \( x \)-coordinates; same \( y \)-coordinate