Question

1. reflection across x = -2

y(-4, 3), x(1, 4), w(1, 2)

Explanation:

Step1: Recall reflection formula

For a point \((x,y)\) reflected across the vertical line \(x = a\), the new \(x\)-coordinate \(x'\) is given by \(x'=2a - x\), and the \(y\)-coordinate remains the same (\(y' = y\)). Here, \(a=-2\).

Step2: Reflect point \(Y(-4,3)\)

Using the formula \(x' = 2(-2)-(-4)=-4 + 4=0\), \(y' = 3\). So \(Y'\) is \((0,3)\).

Step3: Reflect point \(X(1,4)\)

\(x'=2(-2)-1=-4 - 1=-5\), \(y' = 4\). So \(X'\) is \((-5,4)\).

Step4: Reflect point \(W(1,2)\)

\(x'=2(-2)-1=-4 - 1=-5\), \(y' = 2\). So \(W'\) is \((-5,2)\).

Answer:

Reflected points: \(Y'(0,3)\), \(X'(-5,4)\), \(W'(-5,2)\)