Question

1. reflection across the y - axis

Explanation:

To solve the reflection of a figure across the \( y \)-axis, we use the rule for reflecting a point \((x, y)\) across the \( y \)-axis: the new coordinates become \((-x, y)\) (the \( y \)-coordinate remains the same, and the \( x \)-coordinate is negated).

Step 1: Identify Original Coordinates

First, we determine the coordinates of the vertices of the original figure (let's assume the original vertices are \( I \), \( K \), \( N \), \( M \); we'll find their coordinates from the grid):

• Let’s assume \( I = (-3, 4) \) (3 units left of \( y \)-axis, 4 up)
• \( K = (-3, 3) \) (3 left, 3 up)
• \( N = (0, 0) \) (on \( y \)-axis, origin)
• \( M = (1, 3) \) (1 right, 3 up)

Step 2: Apply Reflection Rule

For each vertex, reflect across the \( y \)-axis (use \((x, y) \to (-x, y)\)):

• \( I(-3, 4) \to I'(3, 4) \) (negate \( x \): \(-(-3) = 3\), \( y \) stays 4)
• \( K(-3, 3) \to K'(3, 3) \) (negate \( x \): \(-(-3) = 3\), \( y \) stays 3)
• \( N(0, 0) \to N'(0, 0) \) (negate \( 0 \) is still \( 0 \))
• \( M(1, 3) \to M'(-1, 3) \) (negate \( x \): \(-1\), \( y \) stays 3)

Step 3: Plot Reflected Points

Plot the new points \( I'(3, 4) \), \( K'(3, 3) \), \( N'(0, 0) \), \( M'(-1, 3) \) and connect them to form the reflected figure.

(Note: If the original vertices in the image differ, adjust coordinates accordingly, but the reflection rule remains \( (x, y) \to (-x, y) \).)

The reflected figure will have vertices at \( (3, 4) \), \( (3, 3) \), \( (0, 0) \), and \( (-1, 3) \) (or adjusted based on the exact grid positions).

\(\boldsymbol{\text{Final Answer:}}\) The reflected figure has vertices at \( (3, 4) \), \( (3, 3) \), \( (0, 0) \), and \( (-1, 3) \) (or equivalent, depending on original coordinates). To draw it, plot these points and connect them.

Answer:

To solve the reflection of a figure across the \( y \)-axis, we use the rule for reflecting a point \((x, y)\) across the \( y \)-axis: the new coordinates become \((-x, y)\) (the \( y \)-coordinate remains the same, and the \( x \)-coordinate is negated).

Step 1: Identify Original Coordinates

First, we determine the coordinates of the vertices of the original figure (let's assume the original vertices are \( I \), \( K \), \( N \), \( M \); we'll find their coordinates from the grid):

• Let’s assume \( I = (-3, 4) \) (3 units left of \( y \)-axis, 4 up)
• \( K = (-3, 3) \) (3 left, 3 up)
• \( N = (0, 0) \) (on \( y \)-axis, origin)
• \( M = (1, 3) \) (1 right, 3 up)

Step 2: Apply Reflection Rule

For each vertex, reflect across the \( y \)-axis (use \((x, y) \to (-x, y)\)):

• \( I(-3, 4) \to I'(3, 4) \) (negate \( x \): \(-(-3) = 3\), \( y \) stays 4)
• \( K(-3, 3) \to K'(3, 3) \) (negate \( x \): \(-(-3) = 3\), \( y \) stays 3)
• \( N(0, 0) \to N'(0, 0) \) (negate \( 0 \) is still \( 0 \))
• \( M(1, 3) \to M'(-1, 3) \) (negate \( x \): \(-1\), \( y \) stays 3)

Step 3: Plot Reflected Points

Plot the new points \( I'(3, 4) \), \( K'(3, 3) \), \( N'(0, 0) \), \( M'(-1, 3) \) and connect them to form the reflected figure.

(Note: If the original vertices in the image differ, adjust coordinates accordingly, but the reflection rule remains \( (x, y) \to (-x, y) \).)

The reflected figure will have vertices at \( (3, 4) \), \( (3, 3) \), \( (0, 0) \), and \( (-1, 3) \) (or adjusted based on the exact grid positions).

\(\boldsymbol{\text{Final Answer:}}\) The reflected figure has vertices at \( (3, 4) \), \( (3, 3) \), \( (0, 0) \), and \( (-1, 3) \) (or equivalent, depending on original coordinates). To draw it, plot these points and connect them.