Question

triangles twh and gmb are shown below. determine a sequence of transformation that will result in triangle twh, with vertices t(-1, -6), w(-5, -2), h(3, -3) being mapped onto the triangle gmb with vertices (10, 3), m(6, -1) and b(14, 0).

reflect triangle twh over the y - axis, then translate it 11 units to the right and 3 units up.
translate triangle twh 11 units to the right and 4 units up then reflect it over the y - axis.
reflect triangle twh over the x - axis, then translate it 11 units to the right and 3 units down.
translate triangle twh 11 units to the right and 4 units up then reflect it over the x - axis.

Explanation:

Step1: Reflect over the x - axis

When reflecting a point \((x,y)\) over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\).
For point \(T(-1,-6)\), after reflection over the \(x\) - axis, it becomes \(T'(-1,6)\).
For point \(W(-5,-2)\), after reflection over the \(x\) - axis, it becomes \(W'(-5,2)\).
For point \(H(3,-3)\), after reflection over the \(x\) - axis, it becomes \(H'(3,3)\).

Step2: Translate

The translation rule is \((x,y)\to(x + a,y + b)\).
We want to map \((-1,6)\) to \(G(10,3)\), \((-5,2)\) to \(M(6,-1)\) and \((3,3)\) to \(B(14,0)\).
For the \(x\) - coordinate: \(x\) - coordinate of \(T'\) is \(-1\), \(x\) - coordinate of \(G\) is \(10\), so \(a=10-(-1)=11\).
For the \(y\) - coordinate: \(y\) - coordinate of \(T'\) is \(6\), \(y\) - coordinate of \(G\) is \(3\), so \(b = 3 - 6=-3\).
The translation rule is \((x,y)\to(x + 11,y-3)\)

Answer:

Reflect triangle \(TWH\) over the \(x\) - axis, then translate it \(11\) units to the right and \(3\) units down.