Question

graph the image of △lmn after a reflection over the y-axis.

Explanation:

Step1: Identify original coordinates

First, find the coordinates of points \( L \), \( M \), and \( N \) from the graph.

• Point \( L \): From the grid, \( L \) is at \( (-8, -6) \).
• Point \( M \): \( M \) is at \( (-8, 4) \).
• Point \( N \): \( N \) is at \( (-6, -6) \).

Step2: Apply reflection over y - axis rule

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

• For point \( L(-8, -6) \): Applying the rule, the reflected point \( L' \) is \( (8, -6) \) (since \( -(-8)=8 \) and the \( y \) - coordinate remains \( -6 \)).
• For point \( M(-8, 4) \): Applying the rule, the reflected point \( M' \) is \( (8, 4) \) (since \( -(-8) = 8 \) and the \( y \) - coordinate remains \( 4 \)).
• For point \( N(-6, -6) \): Applying the rule, the reflected point \( N' \) is \( (6, -6) \) (since \( -(-6)=6 \) and the \( y \) - coordinate remains \( -6 \)).

Step3: Graph the reflected points

Plot the points \( L'(8, -6) \), \( M'(8, 4) \), and \( N'(6, -6) \) on the coordinate plane and connect them to form the reflected triangle \( \triangle L'M'N' \).

Answer:

The image of \( \triangle LMN \) after reflection over the \( y \) - axis has vertices at \( L'(8, -6) \), \( M'(8, 4) \), and \( N'(6, -6) \). (To graph, plot these points and connect them.)