which statements are true about trapezoid abcd and its translated image, abcd? select two options.□ the rule…

which statements are true about trapezoid abcd and its translated image, abcd? select two options.□ the rule for the translation can be written as $t_{-3,1}(x, y)$.□ the rule for the translation can be written as $t_{-1,3}(x, y)$.□ the rule for the translation can be written as $(x, y) \\to (x + 1, y - 3)$.□ the rule for the translation can be written as $(x, y) \\to (x - 3, y + 1)$.□ trapezoid abcd has been translated 3 units to the right and 1 unit up.

which statements are true about trapezoid abcd and its translated image, abcd? select two options.□ the rule for the translation can be written as $t_{-3,1}(x, y)$.□ the rule for the translation can be written as $t_{-1,3}(x, y)$.□ the rule for the translation can be written as $(x, y) \\to (x + 1, y - 3)$.□ the rule for the translation can be written as $(x, y) \\to (x - 3, y + 1)$.□ trapezoid abcd has been translated 3 units to the right and 1 unit up.

Answer

Explanation:

Step1: Pick a vertex for comparison

Choose vertex A of trapezoid ABCD: its coordinates are $(0, -2)$. Vertex A' of the translated image has coordinates $(-3, -1)$.

Step2: Calculate horizontal translation

Find the change in x-value: $x' - x = -3 - 0 = -3$. This means a shift of 3 units left, or $x \to x - 3$.

Step3: Calculate vertical translation

Find the change in y-value: $y' - y = -1 - (-2) = 1$. This means a shift of 1 unit up, or $y \to y + 1$.

Step4: Match to translation rules

The translation rule is $(x, y) \to (x - 3, y + 1)$, which is equivalent to $T_{-3, 1}(x, y)$. Verify with another vertex (e.g., B: $(2, -2)$ to B': $(-1, -1)$: $2-3=-1$, $-2+1=-1$, which is correct).

Answer:

  • The rule for the translation can be written as $T_{-3, 1}(x, y)$.
  • The rule for the translation can be written as $(x, y) \to (x - 3, y + 1)$.