Question

transformations test (topic 4) which of the following describes the effect of the transformation given below on points in the coordinate plane?
$(x, y) \to (-x, y)$

• it reflects them across the x-axis
• it rotates them 180 degrees clockwise about the origin
• it rotates them 90 degrees counterclockwise about the origin
• it reflects them across the y-axis

Explanation:

To determine the transformation \((x, y) \to (-x, y)\), we analyze each option:

• Reflecting across the \(x\)-axis changes \((x, y)\) to \((x, -y)\), so the first option is incorrect.
• Rotating 180 degrees clockwise about the origin changes \((x, y)\) to \((-x, -y)\), so the second option is incorrect.
• Rotating 90 degrees counterclockwise about the origin changes \((x, y)\) to \((-y, x)\), so the third option is incorrect.
• Reflecting across the \(y\)-axis changes the sign of the \(x\)-coordinate while keeping the \(y\)-coordinate the same, which matches \((x, y) \to (-x, y)\).

Answer:

it reflects them across the y - axis