Question

d. list the ordered pairs of quadrilateral 1 if it is reflected over the x-axis. explain how you can determine the ordered pairs of the reflection without graphing it. plot the reflection described, and label the figure as 4.

Explanation:

To solve this, we first need the original ordered pairs of Quadrilateral 1 (not provided here). However, the rule for reflecting over the \( x \)-axis is: for a point \( (x, y) \), its reflection over the \( x \)-axis is \( (x, -y) \).

Step 1: Recall the reflection rule

When reflecting a point \( (x, y) \) over the \( x \)-axis, the \( x \)-coordinate remains the same, and the \( y \)-coordinate is multiplied by \( -1 \). So, \( (x, y)
ightarrow (x, -y) \).

Step 2: Apply the rule to each vertex

Suppose Quadrilateral 1 has vertices \( (x_1, y_1) \), \( (x_2, y_2) \), \( (x_3, y_3) \), \( (x_4, y_4) \). Their reflections over the \( x \)-axis would be:
\( (x_1, -y_1) \), \( (x_2, -y_2) \), \( (x_3, -y_3) \), \( (x_4, -y_4) \).

To plot the reflection (Figure 4):

1. Identify the original vertices of Quadrilateral 1.
2. For each vertex, apply the \( (x, y)

ightarrow (x, -y) \) transformation.

1. Plot the new points and connect them to form the reflected quadrilateral, labeling it as Figure 4.

(Note: Without the original coordinates of Quadrilateral 1, we can’t list the specific ordered pairs, but the method above shows how to determine them using the reflection rule over the \( x \)-axis.)

Answer:

To solve this, we first need the original ordered pairs of Quadrilateral 1 (not provided here). However, the rule for reflecting over the \( x \)-axis is: for a point \( (x, y) \), its reflection over the \( x \)-axis is \( (x, -y) \).

Step 1: Recall the reflection rule

When reflecting a point \( (x, y) \) over the \( x \)-axis, the \( x \)-coordinate remains the same, and the \( y \)-coordinate is multiplied by \( -1 \). So, \( (x, y)
ightarrow (x, -y) \).

Step 2: Apply the rule to each vertex

Suppose Quadrilateral 1 has vertices \( (x_1, y_1) \), \( (x_2, y_2) \), \( (x_3, y_3) \), \( (x_4, y_4) \). Their reflections over the \( x \)-axis would be:
\( (x_1, -y_1) \), \( (x_2, -y_2) \), \( (x_3, -y_3) \), \( (x_4, -y_4) \).

To plot the reflection (Figure 4):

1. Identify the original vertices of Quadrilateral 1.
2. For each vertex, apply the \( (x, y)

ightarrow (x, -y) \) transformation.

1. Plot the new points and connect them to form the reflected quadrilateral, labeling it as Figure 4.

(Note: Without the original coordinates of Quadrilateral 1, we can’t list the specific ordered pairs, but the method above shows how to determine them using the reflection rule over the \( x \)-axis.)