Question

write the coordinates of the vertices after a reflection over the y-axis.
t(
,
)
u(
,
)
v(
,
)
w(
,
)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex:

• \( T \): Looking at the graph, \( T \) is at \( (-5, -5) \) (since it's 5 units left on x - axis and 5 units down on y - axis).
• \( U \): \( U \) is at \( (0, - 3) \) (on the y - axis, 3 units down).
• \( V \): \( V \) is at \( (-5, -1) \) (5 units left on x - axis and 1 unit down on y - axis).
• \( W \): \( W \) is at \( (-7, -3) \) (7 units left on x - axis and 3 units down on y - axis).

Step2: Apply reflection over y - axis rule

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

• For \( T(-5, -5) \):

Applying the rule, \( x=-5\to -(-5) = 5 \), \( y=-5 \) remains. So \( T'=(5, -5) \).

• For \( U(0, -3) \):

Applying the rule, \( x = 0\to-0 = 0 \), \( y=-3 \) remains. So \( U'=(0, -3) \).

• For \( V(-5, -1) \):

Applying the rule, \( x=-5\to-(-5)=5 \), \( y = - 1 \) remains. So \( V'=(5, -1) \).

• For \( W(-7, -3) \):

Applying the rule, \( x=-7\to-(-7)=7 \), \( y=-3 \) remains. So \( W'=(7, -3) \).

Answer:

\( T'(5, -5) \), \( U'(0, -3) \), \( V'(5, -1) \), \( W'(7, -3) \)