Question

write the coordinates of the vertices after a reflection over the line $x = 1$.
$b(square,square)$
$c(square,square)$
$d(square,square)$

Explanation:

Step1: Find the reflection formula

For a point \((x,y)\) reflected over the line \(x = a\), the formula is \((2a - x,y)\). Here \(a = 1\), so the formula is \((2\times1 - x,y)=(2 - x,y)\).

Step2: Find the coordinates of \(B'\)

The coordinates of \(B\) are \((0,7)\). Using the formula \((2 - x,y)\), substitute \(x = 0\) and \(y = 7\). Then \(2-0 = 2\), so \(B'=(2,7)\).

Step3: Find the coordinates of \(C'\)

The coordinates of \(C\) are \((9,7)\). Using the formula \((2 - x,y)\), substitute \(x = 9\) and \(y = 7\). Then \(2-9=-7\), so \(C'=(-7,7)\).

Step4: Find the coordinates of \(D'\)

The coordinates of \(D\) are \((0,6)\). Using the formula \((2 - x,y)\), substitute \(x = 0\) and \(y = 6\). Then \(2-0 = 2\), so \(D'=(2,6)\).

Answer:

\(B'(2,7)\)
\(C'(-7,7)\)
\(D'(2,6)\)