Question

1. ( p(0,1) ) write a rule for the translation of ( \triangle lmn ) to ( \triangle lmn ). 9. 10.

Explanation:

Step1: Determine the horizontal translation

Let's assume a point \( (x,y) \) in \( \triangle LMN \). Looking at the \( x - \)coordinates. For example, if we consider the horizontal movement from \( L \) (let's assume \( L \) has \( x - \)coordinate \( x_1\)) to \( L' \) (with \( x - \)coordinate \( x_2\)). The change in the \( x - \)direction: \( x_2=x_1 - 6\) (count the number of units moved along the \( x - \)axis. If we assume a general point \( (x,y) \), the horizontal ( \( x - \)axis) translation is \( x\to x - 6\)).

Step2: Determine the vertical translation

Looking at the \( y - \)coordinates. For example, if we consider the vertical movement from \( L \) (let's assume \( L \) has \( y - \)coordinate \( y_1\)) to \( L' \) (with \( y - \)coordinate \( y_2\)). The change in the \( y - \)direction: \( y_2=y_1+2\) (count the number of units moved along the \( y - \)axis. For a general point \( (x,y) \), the vertical ( \( y - \)axis) translation is \( y\to y + 2\)).

Answer:

The rule for the translation is \( (x,y)\to(x - 6,y + 2)\)