Question

write the coordinates of the vertices after a reflection over the y-axis.

Explanation:

Step1: Find original coordinates

First, determine the original coordinates of points \( K \), \( L \), and \( M \) from the graph.

• For point \( K \): Looking at the grid, it is at \( (-9, 5) \) (since it's 9 units left of the y - axis (x = - 9) and 5 units up (y = 5)).
• For point \( L \): It is on the y - axis, so \( x = 0 \) and \( y = 5 \), so \( L=(0,5) \).
• For point \( M \): It is at \( (-8, 3) \) (8 units left of y - axis, 3 units up).

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 \( K(-9,5) \): Apply the rule, \( x=-9\), so \( -x = 9 \), \( y = 5 \). So \( K'=(9,5) \).
• For \( L(0,5) \): Apply the rule, \( x = 0\), so \( -x=0 \), \( y = 5 \). So \( L'=(0,5) \).
• For \( M(-8,3) \): Apply the rule, \( x=-8\), so \( -x = 8 \), \( y = 3 \). So \( M'=(8,3) \).

Answer:

\( K'(9, 5) \)
\( L'(0, 5) \)
\( M'(8, 3) \)