Question

1. graph the image of abc after a reflection over the x - axis and a translation 4 units right.

Explanation:

Step1: Find coordinates of \(A\), \(B\), \(C\)

From the graph, \(A(-5,3)\), \(B(-2,1)\), \(C(-5,1)\)

Step2: Reflect over \(x -\)axis

The rule for reflection over \(x -\)axis is \((x,y)\to(x,-y)\).
For \(A(-5,3)\), after reflection \(A'(-5,-3)\)
For \(B(-2,1)\), after reflection \(B'(-2,-1)\)
For \(C(-5,1)\), after reflection \(C'(-5,-1)\)

Step3: Translate 4 units right

The rule for translation 4 units right is \((x,y)\to(x + 4,y)\)
For \(A'(-5,-3)\), after translation \(A''(-5+4,-3)=(-1,-3)\)
For \(B'(-2,-1)\), after translation \(B''(-2 + 4,-1)=(2,-1)\)
For \(C'(-5,-1)\), after translation \(C''(-5+4,-1)=(-1,-1)\)

Step4: Plot the new points \(A''(-1,-3)\), \(B''(2,-1)\), \(C''(-1,-1)\) and connect them to form the image of \(\triangle ABC\)

Answer:

Plot the points \(A''(-1,-3)\), \(B''(2,-1)\), \(C''(-1,-1)\) on the coordinate - plane and connect them.