Question

rectangle abcd has vertices a(-6, -2), b(-3, -2), c(-3, -6), and d(-6, -6). the rectangle is translated so that the coordinates of the image are a(-10, 1), b(-7,1), c(-7, -3), and d(-10, -3). which rule was used to translate the image? t_{-4,3}(x,y) t_{-4,1}(x,y) t_{4,-1}(x,y) t_{4,-3}(x,y)

Explanation:

Step1: Analyze x - coordinate change

For point A, the x - coordinate changes from - 6 to - 10. The change in the x - coordinate is $\Delta x=-10 - (-6)=-4$.

Step2: Analyze y - coordinate change

For point A, the y - coordinate changes from - 2 to 1. The change in the y - coordinate is $\Delta y=1-(-2)=3$.

Step3: Determine the translation rule

The general translation rule is $T_{a,b}(x,y)=(x + a,y + b)$, where $a$ is the change in the x - coordinate and $b$ is the change in the y - coordinate. Here, $a=-4$ and $b = 3$, so the rule is $T_{-4,3}(x,y)$.

Answer:

$T_{-4,3}(x,y)$