Question

1. reflect the triangle in the y-axis. then translate 2 units left.

Explanation:

To solve the problem of reflecting the triangle over the \( y \)-axis and then translating it 2 units left, we follow these steps:

Step 1: Identify the original coordinates of the triangle's vertices

From the graph, let's assume the vertices of the triangle are:

• Vertex 1: \( (-2, 3) \)
• Vertex 2: \( (-1, 4) \)
• Vertex 3: \( (0, 2) \)

Step 2: Reflect over the \( y \)-axis

The rule for reflecting a point \( (x, y) \) over the \( y \)-axis is \( (x, y)
ightarrow (-x, y) \).

• For \( (-2, 3) \): \( -(-2) = 2 \), so new point: \( (2, 3) \)
• For \( (-1, 4) \): \( -(-1) = 1 \), so new point: \( (1, 4) \)
• For \( (0, 2) \): \( -(0) = 0 \), so new point: \( (0, 2) \)

Step 3: Translate 2 units left

The rule for translating a point \( (x, y) \) 2 units left is \( (x, y)
ightarrow (x - 2, y) \).

• For \( (2, 3) \): \( 2 - 2 = 0 \), so new point: \( (0, 3) \)
• For \( (1, 4) \): \( 1 - 2 = -1 \), so new point: \( (-1, 4) \)
• For \( (0, 2) \): \( 0 - 2 = -2 \), so new point: \( (-2, 2) \)

Final Vertices After Transformations

The vertices of the triangle after reflection over the \( y \)-axis and translation 2 units left are:

• \( (0, 3) \)
• \( (-1, 4) \)
• \( (-2, 2) \)

To graph the transformed triangle, plot these three points and connect them.

(Note: If the original coordinates were different, adjust the calculations accordingly. The key is applying the reflection and translation rules to each vertex.)

Answer:

To solve the problem of reflecting the triangle over the \( y \)-axis and then translating it 2 units left, we follow these steps:

Step 1: Identify the original coordinates of the triangle's vertices

From the graph, let's assume the vertices of the triangle are:

• Vertex 1: \( (-2, 3) \)
• Vertex 2: \( (-1, 4) \)
• Vertex 3: \( (0, 2) \)

Step 2: Reflect over the \( y \)-axis

The rule for reflecting a point \( (x, y) \) over the \( y \)-axis is \( (x, y)
ightarrow (-x, y) \).

• For \( (-2, 3) \): \( -(-2) = 2 \), so new point: \( (2, 3) \)
• For \( (-1, 4) \): \( -(-1) = 1 \), so new point: \( (1, 4) \)
• For \( (0, 2) \): \( -(0) = 0 \), so new point: \( (0, 2) \)

Step 3: Translate 2 units left

The rule for translating a point \( (x, y) \) 2 units left is \( (x, y)
ightarrow (x - 2, y) \).

• For \( (2, 3) \): \( 2 - 2 = 0 \), so new point: \( (0, 3) \)
• For \( (1, 4) \): \( 1 - 2 = -1 \), so new point: \( (-1, 4) \)
• For \( (0, 2) \): \( 0 - 2 = -2 \), so new point: \( (-2, 2) \)

Final Vertices After Transformations

The vertices of the triangle after reflection over the \( y \)-axis and translation 2 units left are:

• \( (0, 3) \)
• \( (-1, 4) \)
• \( (-2, 2) \)

To graph the transformed triangle, plot these three points and connect them.

(Note: If the original coordinates were different, adjust the calculations accordingly. The key is applying the reflection and translation rules to each vertex.)