Question

1. find the new vertices given the translation properties. triangle abc with vertices a(3, 7), b(7, 10) and c(1, 4); (x, y)→(x - 3,y - 5)

Explanation:

Step1: Apply translation rule to point A

Given $A(3,7)$ and the translation $(x,y)\to(x - 2,y - 4)$. For point A, $x = 3$ and $y=7$. New $x$-coordinate: $3-2 = 1$, new $y$-coordinate: $7 - 4=3$. So $A'(1,3)$.

Step2: Apply translation rule to point B

Given $B(7,0)$ and the translation $(x,y)\to(x - 2,y - 4)$. For point B, $x = 7$ and $y = 0$. New $x$-coordinate: $7-2=5$, new $y$-coordinate: $0 - 4=-4$. So $B'(5,-4)$.

Step3: Apply translation rule to point C

Given $C(1,4)$ and the translation $(x,y)\to(x - 2,y - 4)$. For point C, $x = 1$ and $y = 4$. New $x$-coordinate: $1-2=-1$, new $y$-coordinate: $4 - 4 = 0$. So $C'(-1,0)$.

Answer:

$A'(1,3)$
$B'(5,-4)$
$C'(-1,0)$