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 x - axis. (25 points) * a (-2, 0), b (-4, -3), c (-2, -4), d (0, -3) 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)

Explanation:

Step1: Recall the reflection rule

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

Step2: Apply the rule to each point

• For point \(A(0,2)\):

Using the rule \((x,y)\to(x, - y)\), with \(x = 0\) and \(y=2\), we get \(A'(0,-2)\).

• For point \(B(3,4)\):

Using the rule \((x,y)\to(x, - y)\), with \(x = 3\) and \(y = 4\), we get \(B'(3,-4)\).

• For point \(C(4,2)\):

Using the rule \((x,y)\to(x, - y)\), with \(x = 4\) and \(y=2\), we get \(C'(4,-2)\).

• For point \(D(3,0)\):

Using the rule \((x,y)\to(x, - y)\), with \(x = 3\) and \(y = 0\), we get \(D'(3,0)\) (since \(-0=0\)).

Answer:

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