Question

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.

Explanation:

Step1: Identify translation direction

Take point $A$: original $A(-4,-1)$, image $A'(-1,-2)$.

Step2: Calculate horizontal shift

$\Delta x = -1 - (-4) = 3$ (right 3 units)

Step3: Calculate vertical shift

$\Delta y = -2 - (-1) = -1$ (down 1 unit)

Step4: Match translation rules

Translation rule: $(x,y)\to(x+3,y-1)$, which is $T_{3,-1}(x,y)$.

Step5: Verify options

Check each option against calculated shift.

Answer:

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