Question

4 a. reflect quadrilateral a over the x-axis. label the image quadrilateral b. reflect quadrilateral b over the y-axis. label the image c.

Explanation:

Step1: Reflect over x - axis (Quadrilateral A to B)

To reflect a point \((x,y)\) over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\). First, identify the vertices of Quadrilateral A. Let's assume the vertices of A are \(V_1(x_1,y_1)\), \(V_2(x_2,y_2)\), \(V_3(x_3,y_3)\), \(V_4(x_4,y_4)\). Applying the reflection rule, the vertices of B (image of A over \(x\) - axis) will be \(V_1'(x_1, - y_1)\), \(V_2'(x_2, - y_2)\), \(V_3'(x_3, - y_3)\), \(V_4'(x_4, - y_4)\). Plot these new points and connect them to form Quadrilateral B.

Step2: Reflect over y - axis (Quadrilateral B to C)

To reflect a point \((x,y)\) over the \(y\) - axis, the transformation rule is \((x,y)\to(-x,y)\). Take the vertices of Quadrilateral B ( \(V_1'(x_1, - y_1)\), \(V_2'(x_2, - y_2)\), \(V_3'(x_3, - y_3)\), \(V_4'(x_4, - y_4)\)) and apply the reflection rule. The vertices of C (image of B over \(y\) - axis) will be \(V_1''(-x_1, - y_1)\), \(V_2''(-x_2, - y_2)\), \(V_3''(-x_3, - y_3)\), \(V_4''(-x_4, - y_4)\). Plot these new points and connect them to form Quadrilateral C.

(Note: Since the actual coordinates of the vertices of Quadrilateral A are not given numerically, the process involves using the reflection rules for coordinate - plane transformations. If we had specific coordinates, we could calculate the exact positions. For example, if a vertex of A is \((2,3)\), its reflection over \(x\) - axis (for B) is \((2, - 3)\), and then reflection over \(y\) - axis (for C) is \((-2, - 3)\).)

Answer:

To solve the problem, follow these steps:

1. Reflect Quadrilateral A over the \(x\) - axis to get B:

• For each vertex \((x,y)\) of A, the corresponding vertex of B is \((x, - y)\). Plot these new vertices and connect them to form Quadrilateral B.

1. Reflect Quadrilateral B over the \(y\) - axis to get C:

• For each vertex \((x,y)\) of B, the corresponding vertex of C is \((-x,y)\). Plot these new vertices and connect them to form Quadrilateral C.

(The final answer is the graphical representation of Quadrilaterals B and C obtained by applying the above reflection rules to Quadrilateral A.)