Question

choose the general rule below that describes the translation mapping △abc to △abc. (x,y)→(8x,5y) (x,y)→(x - 5,y - 8) (x,y)→(-8x,-5y) (x,y)→(-5x,-8y) (x,y)→(x + 5,y + 8) (x,y)→(5x,8y) (x,y)→(x + 8,y + 5) (x,y)→(x - 8,y - 5)

Explanation:

Step1: Recall translation rule

In a translation, the general form for moving a point $(x,y)$ is $(x + a,y + b)$, where $a$ is the horizontal displacement and $b$ is the vertical displacement.

Step2: Analyze options

Options like $(x,y)\to(8x,5y)$ etc. are not translations as they involve scaling. Translations only add or subtract values from $x$ and $y$. A translation of a point $(x,y)$ to a new point $(x + a,y + b)$ means moving $a$ units horizontally and $b$ units vertically. For example, $(x,y)\to(x - 5,y - 8)$ moves the point 5 units to the left and 8 units down.

Answer:

Without seeing the actual graph to determine the horizontal and vertical displacements, we can't pick a definite answer from the given options. But the correct form of a translation rule from the options would be one of the form $(x,y)\to(x + a,y + b)$ or $(x,y)\to(x - a,y - b)$ such as $(x,y)\to(x - 5,y - 8)$ or $(x,y)\to(x + 5,y + 8)$ etc.