Question

mn is reflected across the y-axis to form figure jklmn

1. what are the coordinates of the vertices of figure jklmn?

label the vertices with the correct ordered pairs.
j ( , )
k ( , )
l ( , )
m ( , )
n ( , )

Explanation:

To find the coordinates of the vertices after reflecting across the \( y \)-axis, we use the reflection rule: for a point \((x, y)\), its reflection across the \( y \)-axis is \((-x, y)\).

Step 1: Identify original coordinates (from the graph)

• Let's assume the original coordinates (estimating from the grid):
• \( J \): Let's say \( J = (-0, 4) \) (wait, looking at the grid, maybe original \( J \) is \( (0, 4) \)? Wait, maybe better to check:
• Wait, original figure: Let's assume (from typical grid):
• \( J \): \( (0, 4) \)
• \( K \): \( (1, 3) \)
• \( L \): \( (3, 3) \)
• \( M \): \( (4, 1) \)
• \( N \): \( (1, 1) \)

Step 2: Apply reflection over \( y \)-axis (\((x,y) \to (-x,y)\))

• For \( J(0, 4) \): Reflecting over \( y \)-axis: \( ( -0, 4 ) = (0, 4) \), so \( J' = (0, 4) \)
• For \( K(1, 3) \): Reflecting over \( y \)-axis: \( (-1, 3) \), so \( K' = (-1, 3) \)
• For \( L(3, 3) \): Reflecting over \( y \)-axis: \( (-3, 3) \), so \( L' = (-3, 3) \)
• For \( M(4, 1) \): Reflecting over \( y \)-axis: \( (-4, 1) \), so \( M' = (-4, 1) \)
• For \( N(1, 1) \): Reflecting over \( y \)-axis: \( (-1, 1) \), so \( N' = (-1, 1) \)

Wait, maybe the original coordinates were different. Let's re-examine the graph (since the grid is there). Let's check the original points:

Looking at the graph (left side):

• \( J \): at \( x=0 \), \( y=4 \) (so \( (0,4) \))
• \( K \): at \( x=1 \), \( y=3 \) (so \( (1,3) \))
• \( L \): at \( x=3 \), \( y=3 \) (so \( (3,3) \))
• \( M \): at \( x=4 \), \( y=1 \) (so \( (4,1) \))
• \( N \): at \( x=1 \), \( y=1 \) (so \( (1,1) \))

Reflecting over \( y \)-axis: the rule is \( (x, y) \to (-x, y) \). So:

• \( J(0,4) \to (0,4) \) (since \( -0 = 0 \))
• \( K(1,3) \to (-1,3) \)
• \( L(3,3) \to (-3,3) \)
• \( M(4,1) \to (-4,1) \)
• \( N(1,1) \to (-1,1) \)

Answer:

\( J' \): \( (0, 4) \)
\( K' \): \( (-1, 3) \)
\( L' \): \( (-3, 3) \)
\( M' \): \( (-4, 1) \)
\( N' \): \( (-1, 1) \)