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

The rule $T_{- 3,5}(x,y)$ means a translation in the coordinate - plane. The first number in the sub - script represents the horizontal translation and the second number represents the vertical translation.

Step2: Analyze horizontal translation

A value of $-3$ for the first number in the sub - script means a horizontal translation of $3$ units to the left. In terms of the $x$ - coordinate of a point $(x,y)$, the new $x$ - coordinate is $x-3$.

Step3: Analyze vertical translation

A value of $5$ for the second number in the sub - script means a vertical translation of $5$ units up. In terms of the $y$ - coordinate of a point $(x,y)$, the new $y$ - coordinate is $y + 5$.

Step4: Write the translation rule

The translation rule $(x,y)\to(x - 3,y + 5)$.

Answer:

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