Question

write a rule for the translation of $\triangle lmn$ to $\triangle lmn$. (see example 3.)
11)

Explanation:

Step1: Identify key points

Original triangle points: $L(1,-1)$, $M(4,1)$, $N(5,-1)$
Translated points: $L'(-4,1)$, $M'(-1,3)$, $N'(0,1)$

Step2: Calculate horizontal shift

For $x$-coordinate: $\Delta x = x' - x$
$\Delta x = -4 - 1 = -5$, $\Delta x = -1 - 4 = -5$, $\Delta x = 0 - 5 = -5$

Step3: Calculate vertical shift

For $y$-coordinate: $\Delta y = y' - y$
$\Delta y = 1 - (-1) = 2$, $\Delta y = 3 - 1 = 2$, $\Delta y = 1 - (-1) = 2$

Step4: Write translation rule

A point $(x,y)$ shifts left 5, up 2.

Answer:

$(x,y) \to (x - 5, y + 2)$