Question

graph the image of \\( \triangle abc \\) after a reflection over the x - axis and a translation 4 units right.

Explanation:

Step1: Find coordinates of original points

From the graph, \(A(-5,3)\), \(B(-1,1)\), \(C(-5,1)\)

Step2: Reflect over the \(x\)-axis

The rule for reflection over the \(x\)-axis is \((x,y)\to(x, -y)\).
For \(A(-5,3)\): \((-5,3)\to(-5,-3)\)
For \(B(-1,1)\): \((-1,1)\to(-1,-1)\)
For \(C(-5,1)\): \((-5,1)\to(-5,-1)\)

Step3: Translate 4 units right

The rule for translation 4 units right is \((x,y)\to(x + 4,y)\)
For \(A'(-5,-3)\): \((-5+4,-3)=( - 1,-3)\)
For \(B'(-1,-1)\): \((-1 + 4,-1)=(3,-1)\)
For \(C'(-5,-1)\): \((-5+4,-1)=(-1,-1)\)

Step4: Plot the new points

Plot \(A''(-1,-3)\), \(B''(3,-1)\), \(C''(-1,-1)\) and connect them to form the image of \(\triangle ABC\)

Answer:

Plot the points \(A''(-1,-3)\), \(B''(3,-1)\), \(C''(-1,-1)\) and connect them.