Question

1. quadrilateral abcd has coordinates a(0, 2), b(3, 4), c(4, 2), and d(3, 0). determine the coordinates of the vertices of abcd after a reflection in the y - axis. (25 points) *

a (2, 0), b (4, 3), c (2, 4), d (0, 3)
a (0, - 2), b (3, - 4), c (4, - 2), d (3, 0)
a (0, 2), b (- 3, 4), c (- 4, 2), d (- 3, 0)
a (- 2, 0), b (- 4, - 3), c (- 2, - 4), d (0, - 3)

Explanation:

Step1: Recall the reflection rule

When reflecting a point \((x,y)\) over the \(y -\)axis, the rule is \((x,y)\to(-x,y)\).

Step2: Apply the rule to each vertex

• For \(A(0,2)\): Using the rule \((x,y)\to(-x,y)\), when \(x = 0,y=2\), \(-x=0\), so \(A'\) is \((0,2)\).
• For \(B(3,4)\): When \(x = 3,y = 4\), \(-x=-3\), so \(B'\) is \((-3,4)\).
• For \(C(4,2)\): When \(x = 4,y = 2\), \(-x=-4\), so \(C'\) is \((-4,2)\).
• For \(D(3,0)\): When \(x = 3,y = 0\), \(-x=-3\), so \(D'\) is \((-3,0)\).

Answer:

\(A'(0,2),B'(-3,4),C'(-4,2),D'(-3,0)\) (corresponding to the third option in the multiple - choice list)