Question

triangle abc with vertices a(0, 7), b(7, 3), and c(1, 4): (x, y)→(x - 3, y - 4)
a(_, _)
b(_, _)
c(_, _)
find the new vertices given the translation properties.

Explanation:

Step1: Find new vertex A'

Apply the translation $(x,y)\to(x - 3,y - 4)$ to $A(0,7)$. For the x - coordinate of $A'$, $x=0-3=-3$. For the y - coordinate of $A'$, $y = 7-4 = 3$.

Step2: Find new vertex B'

Apply the translation to $B(7,3)$. For the x - coordinate of $B'$, $x=7-3 = 4$. For the y - coordinate of $B'$, $y=3 - 4=-1$.

Step3: Find new vertex C'

Apply the translation to $C(1,4)$. For the x - coordinate of $C'$, $x=1-3=-2$. For the y - coordinate of $C'$, $y=4 - 4=0$.

Answer:

$A'(-3,3)$
$B'(4,-1)$
$C'(-2,0)$