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) → (x + 1, y - 3). the rule for the translation can be written as (x, y) → (x - 3, y + 1). trapezoid abcd has been translated 3 units to the right and 1 unit up.

Explanation:

Step1: Analyze horizontal translation

Observe the x - coordinates of corresponding points. For example, if we look at point A and A', we see that the x - coordinate of A' is 3 less than that of A. In a translation rule \((x,y)\to(x + a,y + b)\), the value of \(a\) represents the horizontal shift. A left - shift of \(n\) units is given by \(a=-n\). Here, \(a = - 3\).

Step2: Analyze vertical translation

Observe the y - coordinates of corresponding points. The y - coordinate of A' is 1 more than that of A. In the translation rule \((x,y)\to(x + a,y + b)\), the value of \(b\) represents the vertical shift. An upward shift of \(n\) units is given by \(b = n\). Here, \(b = 1\). The translation rule is \((x,y)\to(x-3,y + 1)\) which can also be written as \(T_{-3,1}(x,y)\).

Answer:

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