Question

b list the ordered pairs of quadrilateral 1 if it is reflected across the y-axis. explain how you can determine the ordered pairs of the reflection without graphing it. plot the reflection described and label the figure as 2

Explanation:

To solve this, we first need the original ordered pairs of Quadrilateral 1 (which are missing here). However, the rule for reflecting a point \((x, y)\) across the \(y\)-axis is to change the sign of the \(x\)-coordinate, so the new ordered pair becomes \((-x, y)\).

Step 1: Recall the reflection rule over the \(y\)-axis

For any point \((x, y)\) in the coordinate plane, reflecting it across the \(y\)-axis transforms it to \((-x, y)\). This is because the \(y\)-axis is the vertical line \(x = 0\), and reflecting over it flips the horizontal (left-right) position while keeping the vertical (up-down) position the same.

Step 2: Apply the rule to each vertex of Quadrilateral 1

Suppose the original vertices of Quadrilateral 1 are, for example, \((x_1, y_1)\), \((x_2, y_2)\), \((x_3, y_3)\), \((x_4, y_4)\). After reflection over the \(y\)-axis, the new ordered pairs (for Quadrilateral 2) would be \((-x_1, y_1)\), \((-x_2, y_2)\), \((-x_3, y_3)\), \((-x_4, y_4)\).

Step 3: Plot the reflected points

Using the new ordered pairs from Step 2, plot each point on the coordinate plane and connect them to form Quadrilateral 2.

Since the original coordinates of Quadrilateral 1 are not provided, we can’t list the exact ordered pairs. But the process is:

1. Identify original vertices \((x, y)\).
2. Apply \((x, y) \to (-x, y)\) to each.
3. Plot the new points and label as Quadrilateral 2.

If we assume sample original vertices (e.g., \((2, 3)\), \((4, 1)\), \((2, -1)\), \((0, 1)\)), the reflected pairs would be \((-2, 3)\), \((-4, 1)\), \((-2, -1)\), \((0, 1)\).

Answer:

To solve this, we first need the original ordered pairs of Quadrilateral 1 (which are missing here). However, the rule for reflecting a point \((x, y)\) across the \(y\)-axis is to change the sign of the \(x\)-coordinate, so the new ordered pair becomes \((-x, y)\).

Step 1: Recall the reflection rule over the \(y\)-axis

For any point \((x, y)\) in the coordinate plane, reflecting it across the \(y\)-axis transforms it to \((-x, y)\). This is because the \(y\)-axis is the vertical line \(x = 0\), and reflecting over it flips the horizontal (left-right) position while keeping the vertical (up-down) position the same.

Step 2: Apply the rule to each vertex of Quadrilateral 1

Suppose the original vertices of Quadrilateral 1 are, for example, \((x_1, y_1)\), \((x_2, y_2)\), \((x_3, y_3)\), \((x_4, y_4)\). After reflection over the \(y\)-axis, the new ordered pairs (for Quadrilateral 2) would be \((-x_1, y_1)\), \((-x_2, y_2)\), \((-x_3, y_3)\), \((-x_4, y_4)\).

Step 3: Plot the reflected points

Using the new ordered pairs from Step 2, plot each point on the coordinate plane and connect them to form Quadrilateral 2.

Since the original coordinates of Quadrilateral 1 are not provided, we can’t list the exact ordered pairs. But the process is:

1. Identify original vertices \((x, y)\).
2. Apply \((x, y) \to (-x, y)\) to each.
3. Plot the new points and label as Quadrilateral 2.

If we assume sample original vertices (e.g., \((2, 3)\), \((4, 1)\), \((2, -1)\), \((0, 1)\)), the reflected pairs would be \((-2, 3)\), \((-4, 1)\), \((-2, -1)\), \((0, 1)\).