Question

Describe the sequence of transformations that demonstrates the congruence between triangle ABC and triangle A´B´C´.

Answer 1

Reflecting over the x axis means to perform the following tranformation:

$(x,y) \to (x,-y)$

So, you maintain the x coordinate, and change the sign of the y coordinate. The vertices become

$A=(-4, 4)\to \hat{A} = (-4,-4),\quad B=(-2, 3)\to \hat{B} = (-2,-3),\quad C=(0, 7) \to \hat{C}=(0,-7)$

Translating 3 units to the left means to perform the following transformation:

$(x,y) \to (x-3,y)$

So, you maintain the y coordinate, and decrease the x coordinate by 3. The vertices become

$\hat{A} = (-4,-4) \to (-7,-4),\quad \hat{B} = (-2,-3)\to (-5,-3),\quad \hat{C}=(0,-7)\to (-3,-7)$

So, as you can see, after these two transformation, the vertices A, B and C become A', B' and C'.