Question

the dashed figure is the image of the solid figure. what is the algebraic notation for the translation? (x, y) --> (x + 8, y + 6) (x, y) --> (x - 6, y + 8) (x, y) --> (x + 6, y - 8) (x, y) --> (6x, 8y)

Explanation:

Step1: Observe horizontal movement

Count the number of units the solid - figure moves horizontally to get to the dashed - figure. If it moves to the right, the x - value in the translation rule increases; if it moves to the left, the x - value decreases.

Step2: Observe vertical movement

Count the number of units the solid - figure moves vertically to get to the dashed - figure. If it moves up, the y - value in the translation rule increases; if it moves down, the y - value decreases.

Step3: Determine the translation rule

Let's assume the solid figure moves 6 units to the right and 8 units down. The algebraic notation for a translation is \((x,y)\to(x + a,y + b)\), where \(a\) is the horizontal displacement and \(b\) is the vertical displacement. Here, \(a = 6\) (right is positive) and \(b=-8\) (down is negative), so the translation rule is \((x,y)\to(x + 6,y - 8)\)

Answer:

\((x,y)\to(x + 6,y - 8)\)