Question

the vertices of △abc are a(1, - 4), b(-1, - 4), and c(3,3). for the translation below, give the vertices of △abc
t_(-1, - 2)(△abc)
the vertices of △abc are a□, b□, and c□. (simplify your answers. type ordered pairs.)

Explanation:

Step1: Recall translation rule

A translation $T_{(a,b)}$ moves a point $(x,y)$ to $(x + a,y + b)$. Here $a=-1$ and $b = - 2$.

Step2: Find coordinates of $A'$

For point $A(1,-4)$, $x = 1$ and $y=-4$. Then $x'=1+( - 1)=0$ and $y'=-4+( - 2)=-6$. So $A'=(0,-6)$.

Step3: Find coordinates of $B'$

For point $B(-1,-4)$, $x=-1$ and $y = - 4$. Then $x'=-1+( - 1)=-2$ and $y'=-4+( - 2)=-6$. So $B'=(-2,-6)$.

Step4: Find coordinates of $C'$

For point $C(3,3)$, $x = 3$ and $y = 3$. Then $x'=3+( - 1)=2$ and $y'=3+( - 2)=1$. So $C'=(2,1)$.

Answer:

$A'(0,-6), B'(-2,-6), C'(2,1)$