Question

with the skills
l abcd. appropriately label the vertices.
b. reflect across ( x = 1 )

Explanation:

To solve the reflection of a figure across the vertical line \( x = 1 \), we follow these steps:

Step 1: Identify the coordinates of the original vertices

First, we need to determine the coordinates of the vertices of the original figure (let's assume the original vertices are \( A(x_1, y_1) \), \( B(x_2, y_2) \), \( C(x_3, y_3) \), \( D(x_4, y_4) \) from the graph). For example, if we assume the original vertices (from the grid) are:

• Let’s say \( A(-3, 4) \), \( B(-5, 2) \), \( C(-2, 1) \), \( D(-1, 2) \) (these are approximate based on the grid; actual coordinates depend on the graph).

Step 2: Recall the reflection formula across \( x = a \)

The formula for reflecting a point \( (x, y) \) across the vertical line \( x = a \) is:
\[
(x', y') = (2a - x, y)
\]
Here, \( a = 1 \), so the formula becomes:
\[
(x', y') = (2(1) - x, y) = (2 - x, y)
\]

Step 3: Apply the reflection formula to each vertex

For vertex \( A(-3, 4) \):

\[
x' = 2 - (-3) = 5, \quad y' = 4
\]
So, the reflected vertex \( A' \) is \( (5, 4) \).

For vertex \( B(-5, 2) \):

\[
x' = 2 - (-5) = 7, \quad y' = 2
\]
So, the reflected vertex \( B' \) is \( (7, 2) \).

For vertex \( C(-2, 1) \):

\[
x' = 2 - (-2) = 4, \quad y' = 1
\]
So, the reflected vertex \( C' \) is \( (4, 1) \).

For vertex \( D(-1, 2) \):

\[
x' = 2 - (-1) = 3, \quad y' = 2
\]
So, the reflected vertex \( D' \) is \( (3, 2) \).

Step 4: Plot the reflected vertices and draw the figure

Plot the points \( A'(5, 4) \), \( B'(7, 2) \), \( C'(4, 1) \), \( D'(3, 2) \) on the coordinate plane and connect them to form the reflected figure \( A'B'C'D' \).

Final Answer

The reflected vertices across \( x = 1 \) are:

• \( A' = (5, 4) \)
• \( B' = (7, 2) \)
• \( C' = (4, 1) \)
• \( D' = (3, 2) \)

(Note: The actual coordinates may vary slightly depending on the exact position of the original vertices on the grid. The key is to apply the reflection formula \( (2 - x, y) \) to each original vertex.)

Answer:

To solve the reflection of a figure across the vertical line \( x = 1 \), we follow these steps:

Step 1: Identify the coordinates of the original vertices

First, we need to determine the coordinates of the vertices of the original figure (let's assume the original vertices are \( A(x_1, y_1) \), \( B(x_2, y_2) \), \( C(x_3, y_3) \), \( D(x_4, y_4) \) from the graph). For example, if we assume the original vertices (from the grid) are:

• Let’s say \( A(-3, 4) \), \( B(-5, 2) \), \( C(-2, 1) \), \( D(-1, 2) \) (these are approximate based on the grid; actual coordinates depend on the graph).

Step 2: Recall the reflection formula across \( x = a \)

The formula for reflecting a point \( (x, y) \) across the vertical line \( x = a \) is:
\[
(x', y') = (2a - x, y)
\]
Here, \( a = 1 \), so the formula becomes:
\[
(x', y') = (2(1) - x, y) = (2 - x, y)
\]

Step 3: Apply the reflection formula to each vertex

For vertex \( A(-3, 4) \):

\[
x' = 2 - (-3) = 5, \quad y' = 4
\]
So, the reflected vertex \( A' \) is \( (5, 4) \).

For vertex \( B(-5, 2) \):

\[
x' = 2 - (-5) = 7, \quad y' = 2
\]
So, the reflected vertex \( B' \) is \( (7, 2) \).

For vertex \( C(-2, 1) \):

\[
x' = 2 - (-2) = 4, \quad y' = 1
\]
So, the reflected vertex \( C' \) is \( (4, 1) \).

For vertex \( D(-1, 2) \):

\[
x' = 2 - (-1) = 3, \quad y' = 2
\]
So, the reflected vertex \( D' \) is \( (3, 2) \).

Step 4: Plot the reflected vertices and draw the figure

Plot the points \( A'(5, 4) \), \( B'(7, 2) \), \( C'(4, 1) \), \( D'(3, 2) \) on the coordinate plane and connect them to form the reflected figure \( A'B'C'D' \).

Final Answer

The reflected vertices across \( x = 1 \) are:

• \( A' = (5, 4) \)
• \( B' = (7, 2) \)
• \( C' = (4, 1) \)
• \( D' = (3, 2) \)

(Note: The actual coordinates may vary slightly depending on the exact position of the original vertices on the grid. The key is to apply the reflection formula \( (2 - x, y) \) to each original vertex.)