Question

select the correct answer from each drop - down menu.
a sequence of transformations maps (\triangle abc) to (\triangle abc). the first transformation is a reflection across the x - axis followed by a translation 4 units to the right and 10 units up, 8 units to the right and 4 units up, 10 units to the right and 2 units up, 10 units to the right and 4 units up.

Explanation:

Step1: Analyze reflection

Reflecting a point \((x,y)\) across the \(x -\)axis gives \((x,-y)\).

Step2: Analyze translation

Let's assume a general point \((x,y)\) after reflection across \(x -\)axis is \((x,-y)\). Then for translation, if we move a point \((x,-y)\) \(a\) units right (add \(a\) to \(x\) - coordinate) and \(b\) units up (add \(b\) to \(y\) - coordinate).
Take point \(A(-6,2)\), after reflection across \(x -\)axis it is \((-6,-2)\). Then if we translate \((-6,-2)\) \(10\) units right (\(x=-6 + 10=4\)) and \(4\) units up (\(y=-2+4 = 2\)).
Take point \(B(-3,6)\), after reflection across \(x -\)axis it is \((-3,-6)\). Then translate \((-3,-6)\) \(10\) units right (\(x=-3 + 10 = 7\)) and \(4\) units up (\(y=-6+4=-2\)).
Take point \(C(-4,2)\), after reflection across \(x -\)axis it is \((-4,-2)\). Then translate \((-4,-2)\) \(10\) units right (\(x=-4+10 = 6\)) and \(4\) units up (\(y=-2 + 4=2\)).

So the sequence of transformations that maps \(\triangle ABC\) to \(\triangle A'B'C'\) is a reflection across the \(x -\)axis followed by a translation \(10\) units to the right and \(4\) units up.

Answer:

x - axis; 10 units to the right and 4 units up