Question

write the coordinates of the vertices after a reflection over the line $x = 1$.

Explanation:

Step1: Recall the reflection formula

The formula for reflecting a point \((x,y)\) over the line \(x = a\) is \((2a - x,y)\). Here \(a = 1\).

Step2: Find the coordinates of each vertex after reflection

• For point \(B(2,-6)\):

Using the formula \(x'=2\times1 - 2=0\), \(y'=-6\). So the new coordinate is \((0,-6)\).

• For point \(E(3,1)\):

Using the formula \(x'=2\times1 - 3=-1\), \(y' = 1\). So the new coordinate is \((-1,1)\).

• For point \(D(5,1)\):

Using the formula \(x'=2\times1 - 5=-3\), \(y'=1\). So the new coordinate is \((-3,1)\).

• For point \(C(9,-6)\):

Using the formula \(x'=2\times1 - 9=-7\), \(y'=-6\). So the new coordinate is \((-7,-6)\).

Answer:

\(B'(0,-6)\), \(E'(-1,1)\), \(D'(-3,1)\), \(C'(-7,-6)\)