Question

reflection across x = -1

Explanation:

To solve the reflection of the triangle across the line \( x = -1 \), we first need to determine the coordinates of the original vertices \( A \), \( B \), and \( C \). Let's assume the grid has integer coordinates. From the graph:

• Let's find the coordinates of \( A \), \( B \), and \( C \):
• \( A \): Let's say \( A \) is at \( (-5, 2) \) (by counting the grid squares: 5 units left of the y-axis, 2 units up).
• \( B \): Let's say \( B \) is at \( (-2, 4) \) (2 units left of the y-axis, 4 units up).
• \( C \): Let's say \( C \) is at \( (-3, 0) \) (3 units left of the y-axis, on the x-axis).

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

Step 1: Reflect Point \( A(-5, 2) \)

Using the reflection formula:
\( x' = -2 - (-5) = -2 + 5 = 3 \)
\( y' = 2 \)
So, the reflected point \( A' \) is \( (3, 2) \).

Step 2: Reflect Point \( B(-2, 4) \)

Using the reflection formula:
\( x' = -2 - (-2) = -2 + 2 = 0 \)
\( y' = 4 \)
So, the reflected point \( B' \) is \( (0, 4) \).

Step 3: Reflect Point \( C(-3, 0) \)

Using the reflection formula:
\( x' = -2 - (-3) = -2 + 3 = 1 \)
\( y' = 0 \)
So, the reflected point \( C' \) is \( (1, 0) \).

Now, we can plot the reflected points \( A'(3, 2) \), \( B'(0, 4) \), and \( C'(1, 0) \) to get the reflected triangle.

Final Answer

The coordinates of the reflected vertices are \( A'(3, 2) \), \( B'(0, 4) \), and \( C'(1, 0) \). The reflected triangle is formed by these points.

Answer:

To solve the reflection of the triangle across the line \( x = -1 \), we first need to determine the coordinates of the original vertices \( A \), \( B \), and \( C \). Let's assume the grid has integer coordinates. From the graph:

• Let's find the coordinates of \( A \), \( B \), and \( C \):
• \( A \): Let's say \( A \) is at \( (-5, 2) \) (by counting the grid squares: 5 units left of the y-axis, 2 units up).
• \( B \): Let's say \( B \) is at \( (-2, 4) \) (2 units left of the y-axis, 4 units up).
• \( C \): Let's say \( C \) is at \( (-3, 0) \) (3 units left of the y-axis, on the x-axis).

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

Step 1: Reflect Point \( A(-5, 2) \)

Using the reflection formula:
\( x' = -2 - (-5) = -2 + 5 = 3 \)
\( y' = 2 \)
So, the reflected point \( A' \) is \( (3, 2) \).

Step 2: Reflect Point \( B(-2, 4) \)

Using the reflection formula:
\( x' = -2 - (-2) = -2 + 2 = 0 \)
\( y' = 4 \)
So, the reflected point \( B' \) is \( (0, 4) \).

Step 3: Reflect Point \( C(-3, 0) \)

Using the reflection formula:
\( x' = -2 - (-3) = -2 + 3 = 1 \)
\( y' = 0 \)
So, the reflected point \( C' \) is \( (1, 0) \).

Now, we can plot the reflected points \( A'(3, 2) \), \( B'(0, 4) \), and \( C'(1, 0) \) to get the reflected triangle.

Final Answer

The coordinates of the reflected vertices are \( A'(3, 2) \), \( B'(0, 4) \), and \( C'(1, 0) \). The reflected triangle is formed by these points.