Question

(b) 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 in the coordinate - plane, the general form of a translation is $(x,y)\to(x + a,y + b)$, where $a$ is the horizontal displacement and $b$ is the vertical displacement. Multiplication of the $x$ and $y$ coordinates like $(x,y)\to(kx,ly)$ ($k
eq1$ and $l
eq1$) represents a dilation, not a translation.

Step2: Analyze options

We need to find the option in the form $(x,y)\to(x + a,y + b)$. Among the given options, the rule $(x,y)\to(x + 5,y + 8)$ is in the correct form of a translation rule where the figure is translated 5 units to the right (since $a = 5>0$) and 8 units up (since $b = 8>0$).

Answer:

$(x,y)\to(x + 5,y + 8)$