Question

writing a rule for a translation. which rule describes the translation? o $t_{-3, -2}(x, y)$ o $t_{-3, 2}(x, y)$ o $t_{3, -2}(x, y)$ o $t_{3, 2}(x, y)$

Explanation:

Step1: Analyze horizontal translation

To find the horizontal translation, look at the change in the x - coordinates of corresponding points. If we take a point on the original figure and its corresponding point on the translated figure, say a vertex of the trapezoid. The original figure moves to the right. Moving to the right means an increase in the x - coordinate. If we assume a point $(x,y)$ on the original figure, the x - coordinate of the corresponding point on the new figure is $x + 3$, so the horizontal translation is 3 units to the right (a positive 3 in the x - direction).

Step2: Analyze vertical translation

To find the vertical translation, look at the change in the y - coordinates of corresponding points. The original figure moves down. Moving down means a decrease in the y - coordinate. If we assume a point $(x,y)$ on the original figure, the y - coordinate of the corresponding point on the new figure is $y-2$, so the vertical translation is 2 units down (a negative 2 in the y - direction).

Step3: Determine the translation rule

The general form of a translation rule is $T_{a,b}(x,y)=(x + a,y + b)$, where $a$ is the horizontal translation and $b$ is the vertical translation. Here, $a = 3$ and $b=-2$, so the translation rule is $T_{3,-2}(x,y)$.

Answer:

$T_{3,-2}(x,y)$