Question

1. triangle xyz with vertices x(-8, 3), y(-6, 5), and z(-5, -2): in the line x = -4

x ( , )
y ( , )
z ( , )

Explanation:

Step1: Recall reflection over vertical line

For a point \((x,y)\) reflected over the line \(x = a\), the new \(x\)-coordinate is \(2a - x\) and \(y\)-coordinate remains \(y\). Here, \(a=-4\).

Step2: Reflect point X(-8,3)

Calculate \(x'\) for \(X\): \(2(-4)-(-8)= -8 + 8 = 0\), \(y' = 3\). So \(X'(0,3)\).

Step3: Reflect point Y(-6,5)

Calculate \(x'\) for \(Y\): \(2(-4)-(-6)= -8 + 6 = -2\), \(y' = 5\). So \(Y'(-2,5)\).

Step4: Reflect point Z(-5,-2)

Calculate \(x'\) for \(Z\): \(2(-4)-(-5)= -8 + 5 = -3\), \(y' = -2\). So \(Z'(-3,-2)\).

Answer:

\(X'(0, 3)\), \(Y'(-2, 5)\), \(Z'(-3, -2)\)