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 the translation rule

The translation rule \(T_{a,b}(x,y)\) means \((x,y)\to(x + a,y + b)\).

Step2: Identify \(a\) and \(b\)

Here \(a=-3\) and \(b = 5\).

Step3: Apply the rule

Substitute \(a=-3\) and \(b = 5\) into \((x,y)\to(x + a,y + b)\), we get \((x,y)\to(x-3,y + 5)\)

Answer:

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