Question

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

A(-4, 4), B(-2, 3) and C(0, 7); A prime(-7, -4), B prime(-5, -3), and C prime(-3, -7).



Reflect over the x-axis and translate 4 units to the right.

Reflect over the x-axis and translate 3 units to the left.

Reflect over the y-axis and translate 1 unit up.

Reflect over the y-axis and translate 3 units down.

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'.