Question

fill in the blank 3 points
△xyz has vertices x(1,1), y(3,2), and z(-1,3). if △xyz is reflected across the x = -1 line, what are the vertices for the reflection image?
x ( type your answer... , type your answer... )
y ( type your answer... , type your answer... )
z ( type your answer... , type your answer... )

Explanation:

Step1: Formula for reflection over \(x = a\)

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

Step2: Find \(X'\)

For \(X(1,1)\), using the formula \(x'=2(-1)-1=-2 - 1=-3\), \(y' = 1\). So \(X'(-3,1)\)

Step3: Find \(Y'\)

For \(Y(3,2)\), \(x'=2(-1)-3=-2-3 = -5\), \(y'=2\). So \(Y'(-5,2)\)

Step4: Find \(Z'\)

For \(Z(-1,3)\), \(x'=2(-1)-(-1)=-2 + 1=-1\), \(y'=3\). So \(Z'(-1,3)\)

Answer:

\(X'(-3,1)\), \(Y'(-5,2)\), \(Z'(-1,3)\)