Question

which type of transformation is described by $(x,y)\to(-x,y)$?
a a reflection across the $y$-axis
b a rotation of $90^{circ}$ about the origin
c a dilation of scale factor $-1$
d a rotation of $180^{circ}$ about the origin

Explanation:

• Reflection across the \(y\) - axis:
• The rule for reflection across the \(y\) - axis is \((x,y)\to(-x,y)\).
• Rotation of \(90^{\circ}\) about the origin:
• The rule for rotation of \(90^{\circ}\) about the origin is \((x,y)\to(-y,x)\).
• Dilation of scale factor \(- 1\):
• The rule for dilation of scale factor \(k\) is \((x,y)\to(kx,ky)\). For \(k = - 1\), it is \((x,y)\to(-x,-y)\).
• Rotation of \(180^{\circ}\) about the origin:
• The rule for rotation of \(180^{\circ}\) about the origin is \((x,y)\to(-x,-y)\).

Answer:

A. a reflection across the \(y\) - axis