Question

a point is translated 3 units left and 4 units up. what is the correct translation rule? t(x,y)→(x - 3,y - 4) t(x,y)→(x - 3,y + 4) t(x,y)→(x + 3,y - 4) t(x,y)→(x + 3,y + 4)

Explanation:

Step1: Understand horizontal translation

Moving left in the coordinate - plane means subtracting from the x - coordinate. If a point is translated 3 units left, the x - coordinate of the original point $(x,y)$ changes to $x - 3$.

Step2: Understand vertical translation

Moving up in the coordinate - plane means adding to the y - coordinate. If a point is translated 4 units up, the y - coordinate of the original point $(x,y)$ changes to $y + 4$.

Step3: Write the translation rule

The translation rule for a point $(x,y)$ that is translated 3 units left and 4 units up is $T(x,y)\to(x - 3,y + 4)$.

Answer:

$T(x,y)\to(x - 3,y + 4)$