Question

write the coordinates of the vertices after a reflection over the line ( x = - 2 ).
( t ^ { prime } ( square, square ) )
( u ^ { prime } ( square, square ) )
( v ^ { prime } ( square, square ) )
( w ^ { prime } ( square, square ) )

Explanation:

Step1: Recall the reflection formula

For a point \((x,y)\) reflected over the line \(x = a\), the formula is \((2a - x,y)\). Here \(a=-2\).

Step2: Find \(T'\)

The coordinates of \(T\) are \((-2,-1)\). Using the formula \(x'=2(-2)-(-2)=-4 + 2=-2\), \(y'=-1\). So \(T'(-2,-1)\)

Step3: Find \(U'\)

The coordinates of \(U\) are \((6,-1)\). Using the formula \(x'=2(-2)-6=-4-6=-10\), \(y'=-1\). So \(U'(-10,-1)\)

Step4: Find \(V'\)

The coordinates of \(V\) are \((6,5)\). Using the formula \(x'=2(-2)-6=-4 - 6=-10\), \(y'=5\). So \(V'(-10,5)\)

Step5: Find \(W'\)

The coordinates of \(W\) are \((-2,5)\). Using the formula \(x'=2(-2)-(-2)=-4 + 2=-2\), \(y'=5\). So \(W'(-2,5)\)

Answer:

\(T'(-2,-1)\)
\(U'(-10,-1)\)
\(V'(-10,5)\)
\(W'(-2,5)\)