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 y = 3 (25 points) *

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)
a (0, 4), b (3, 2), c (4, 4), d (3, 6),

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 = -x. (25 points) *

Explanation:

Step1: Reflection rule for \(y = 3\)

The formula for reflecting a point \((x,y)\) over the line \(y = k\) is \((x,2k - y)\). Here \(k = 3\).

Step2: Apply the rule to each point

• For \(A(0,2)\):

\(x = 0\), \(y=2\). Using the formula \(2k - y=2\times3 - 2=4\). So \(A'(0,4)\)

• For \(B(3,4)\):

\(x = 3\), \(y = 4\). Using the formula \(2k - y=2\times3 - 4 = 2\). So \(B'(3,2)\)

• For \(C(4,2)\):

\(x = 4\), \(y = 2\). Using the formula \(2k - y=2\times3 - 2=4\). So \(C'(4,4)\)

• For \(D(3,0)\):

\(x = 3\), \(y = 0\). Using the formula \(2k - y=2\times3-0 = 6\). So \(D'(3,6)\)

Answer:

\(A'(0,4), B'(3,2), C'(4,4), D'(3,6)\) (the fourth option)