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=-x. (25 points) *

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, 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 formula

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

Step2: Apply the formula to each vertex

• For \(A(0,2)\):

Substitute \(x = 0\) and \(y=2\) into \((-y,-x)\). We get \((-2,0)\)

• For \(B(3,4)\):

Substitute \(x = 3\) and \(y = 4\) into \((-y,-x)\). We get \((-4,-3)\)

• For \(C(4,2)\):

Substitute \(x = 4\) and \(y=2\) into \((-y,-x)\). We get \((-2,-4)\)

• For \(D(3,0)\):

Substitute \(x = 3\) and \(y = 0\) into \((-y,-x)\). We get \((0,-3)\)

Answer:

\(A'(-2,0), B'(-4,-3), C'(-2,-4), D'(0,-3)\)