Question

δabc is reflected across the x - axis and then translated 4 units up to create δabc. what are the coordinates of the vertices of δabc?

Explanation:

Step1: Find original coordinates

From the graph, \(A(-3,1)\), \(B(-1,3)\), \(C(-2,1)\)

Step2: Reflect across x - axis

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is \((x,-y)\).
For \(A(-3,1)\), after reflection \(A_1(-3,-1)\)
For \(B(-1,3)\), after reflection \(B_1(-1,-3)\)
For \(C(-2,1)\), after reflection \(C_1(-2,-1)\)

Step3: Translate 4 units up

The rule for translating a point \((x,y)\) \(4\) units up is \((x,y + 4)\)
For \(A_1(-3,-1)\), \(A'(-3,-1 + 4)=(-3,3)\)
For \(B_1(-1,-3)\), \(B'(-1,-3 + 4)=(-1,1)\)
For \(C_1(-2,-1)\), \(C'(-2,-1+4)=(-2,3)\)

Answer:

\(A'(-3,3)\), \(B'(-1,1)\), \(C'(-2,3)\)