Question

1. rhombus abcd is shown on the coordinate grid below. the designer reflected rhombus abcd across the y-axis to create rhombus abcd. 8.10c

which rule describes this reflection?
a ((x, y)\to(-x, y))
b ((x, y)\to(x, -y))
c ((x, y)\to(-x, -y))
d ((x, y)\to(y, -x))

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is that the \(y\) - coordinate remains the same and the \(x\) - coordinate changes its sign. Mathematically, it is \((x,y)\to(-x,y)\).

Step2: Analyze other options

• Option B: \((x,y)\to(x, - y)\) is the rule for reflection over the \(x\) - axis, not the \(y\) - axis.
• Option C: \((x,y)\to(-x,-y)\) is the rule for reflection over the origin.
• Option D: \((x,y)\to(y, - x)\) is a rotation (90 - degree clockwise rotation), not a reflection over the \(y\) - axis.

Answer:

A. \((x, y)\to(-x, y)\)