Question

triangle efg has vertices e(-3, 4), f(-5, -1), and g(1, 1). the triangle is translated so that the coordinates of the image are e(-1, 0), f(-3, -5), and g(3, -3). which rule was used to translate the image? o t_{4, -4}(x, y) o t_{-4, -4}(x, y) o t_{2, -4}(x, y) o t_{-2, -4}(x, y)

Explanation:

Step1: Find change in x - coordinate

For point E, $x$-coordinate changes from - 3 to - 1. The change is $\Delta x=-1-(-3)=2$.

Step2: Find change in y - coordinate

For point E, $y$-coordinate changes from 4 to 0. The change is $\Delta y = 0 - 4=-4$.

Step3: Determine translation rule

The general translation rule is $T_{a,b}(x,y)=(x + a,y + b)$, where $a$ is the change in $x$ and $b$ is the change in $y$. Here $a = 2$ and $b=-4$, so the rule is $T_{2,-4}(x,y)$.

Answer:

C. $T_{2,-4}(x,y)$