Question

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

$t(\square,\square)$

$u(\square,\square)$

$v(\square,\square)$

$w(\square,\square)$

Explanation:

Step1: Recall the reflection rule

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

Step2: Find the coordinates of \(T\)

The coordinates of \(T\) are \((-5,-4)\). Using the reflection rule \((x,y)\to(x, - y)\), for \(T(-5,-4)\), we get \(T'(-5,4)\) (since \(y=-4\) and \(-y = 4\)).

Step3: Find the coordinates of \(U\)

The coordinates of \(U\) are \((-5,-1)\). Using the reflection rule \((x,y)\to(x, - y)\), for \(U(-5,-1)\), we get \(U'(-5,1)\) (since \(y =- 1\) and \(-y=1\)).

Step4: Find the coordinates of \(V\)

The coordinates of \(V\) are \((-2,-1)\). Using the reflection rule \((x,y)\to(x, - y)\), for \(V(-2,-1)\), we get \(V'(-2,1)\) (since \(y=-1\) and \(-y = 1\)).

Step5: Find the coordinates of \(W\)

The coordinates of \(W\) are \((-2,-4)\). Using the reflection rule \((x,y)\to(x, - y)\), for \(W(-2,-4)\), we get \(W'(-2,4)\) (since \(y=-4\) and \(-y = 4\)).

Answer:

\(T'(-5,4)\), \(U'(-5,1)\), \(V'(-2,1)\), \(W'(-2,4)\)