Question

write the coordinates of the vertices after a reflection over the line ( x = - 1 ).
( b ^ { prime } ( square, square ) )
( c ^ { prime } ( square, square ) )
( d ^ { prime } ( square, square ) )
( e ^ { 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 \(a=-1\).

Step2: Find coordinates of \(B\)

Original coordinates of \(B\) are \((1,-3)\). Using the formula \(x'=2(-1)-1=-2 - 1=-3\), \(y'=-3\). So \(B'(-3,-3)\).

Step3: Find coordinates of \(C\)

Original coordinates of \(C\) are \((8,-2)\). Using the formula \(x'=2(-1)-8=-2 - 8=-10\), \(y'=-2\). So \(C'(-10,-2)\).

Step4: Find coordinates of \(D\)

Original coordinates of \(D\) are \((1,-1)\). Using the formula \(x'=2(-1)-1=-2 - 1=-3\), \(y'=-1\). So \(D'(-3,-1)\).

Step5: Find coordinates of \(E\)

Original coordinates of \(E\) are \((0,-2)\). Using the formula \(x'=2(-1)-0=-2\), \(y'=-2\). So \(E'(-2,-2)\).

Answer:

\(B'(-3,-3)\)
\(C'(-10,-2)\)
\(D'(-3,-1)\)
\(E'(-2,-2)\)