Question

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

Explanation:

Step1: Recall the reflection rule over the y - axis

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

Step2: Find the coordinates of \(U\), \(V\), \(W\)

From the graph, \(U(-6,0)\), \(V(0,0)\), \(W(-2,7)\).

Step3: Apply the reflection rule

For \(U(-6,0)\):
Using the rule \((x,y)\to(-x,y)\), when \(x = - 6\) and \(y = 0\), we get \(U'(6,0)\) (since \(-x=-(-6) = 6\)).
For \(V(0,0)\):
Using the rule \((x,y)\to(-x,y)\), when \(x = 0\) and \(y = 0\), we get \(V'(0,0)\) (since \(-x=-0 = 0\)).
For \(W(-2,7)\):
Using the rule \((x,y)\to(-x,y)\), when \(x=-2\) and \(y = 7\), we get \(W'(2,7)\) (since \(-x=-(-2)=2\)).

Answer:

\(U'(6,0)\), \(V'(0,0)\), \(W'(2,7)\)