Question

a triangle on a coordinate plane is translated according to the rule $t_{-3, 5}(x, y)$. which is another way to write this rule?
$\bigcirc$ $(x,y) \to (x - 3, y + 5)$
$\bigcirc$ $(x,y) \to (x - 3, y - 5)$
$\bigcirc$ $(x,y) \to (x + 3, y - 5)$
$\bigcirc$ $(x,y) \to (x + 3, y + 5)$

Explanation:

Step1: Recall translation rule

The translation rule \( T_{a,b}(x,y) \) means we add \( a \) to the \( x \)-coordinate and \( b \) to the \( y \)-coordinate of the point \((x,y)\), so \( T_{a,b}(x,y)=(x + a,y + b) \).

Step2: Apply the rule to \( T_{-3,5}(x,y) \)

Here, \( a=-3 \) and \( b = 5 \). Substituting into the formula, we get \( (x+(-3),y + 5)=(x - 3,y + 5) \).

Answer:

\((x,y)\to(x - 3,y + 5)\) (the first option)