Question

look at the image below please. this is my homework by the way.predict the result of applying the sequence to transformations to the given figure.

Answer 1

Given the triangle ABC :

The coordinates of the triangle are :

$\begin{gathered} A=(1,4) \\ B=(4,7) \\ C=(4,0) \end{gathered}$

First, translation a long the vector (-1 , -3)

So, the rule of translation will be :

$\begin{gathered} (x,y)\rightarrow(x-1,y-3) \\ so, \\ A^{\prime}=(1,4)+(-1,-3)=(0,1) \\ B^{\prime}=(4,7)+(-1,-3)=(3,4) \\ C^{\prime}=(4,0)+(-1,-3)=(3,-3) \end{gathered}$

Second, Rotation 180 degree about the origin:

The rule of rotation will be :

$\begin{gathered} (x,y)\rightarrow(-x,-y) \\ So, \\ A^{\doubleprime}=(0,-1) \\ B^{\doubleprime}=(-3,-4) \\ C^{\doubleprime}=(-3,3) \end{gathered}$

Finally, dilated with a factor of 2:

So, the rule will be :

$\begin{gathered} (x,y)\rightarrow(rx,ry) \\ r=2 \\ So, \\ A^{\doubleprime\prime}=2\cdot(0,-1)=(0,-2) \\ B^{\doubleprime\prime}=2\cdot(-3,-4)=(-6,-8) \\ C^{\doubleprime\prime}=2\cdot(-3,3)=(-6,6) \end{gathered}$