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?
$(x,y)\to(x - 3,y + 5)$
$(x,y)\to(x - 3,y - 5)$
$(x,y)\to(x + 3,y - 5)$
$(x,y)\to(x + 3,y + 5)$

Explanation:

Step1: Understand translation rule

In the translation rule $T_{- 3,5}(x,y)$, the first number -3 represents the horizontal translation and the second number 5 represents the vertical translation.

Step2: Determine horizontal change

A negative number for the first - coordinate in the translation rule means a left - shift. For the $x$ - coordinate, $x$ changes to $x-3$.

Step3: Determine vertical change

A positive number for the second - coordinate in the translation rule means an up - shift. For the $y$ - coordinate, $y$ changes to $y + 5$.
So the translation rule $(x,y)\to(x - 3,y + 5)$.

Answer:

A. $(x,y)\to(x - 3,y + 5)$