Question

which statements are true about triangle abc and its translated image, abc? select two options. the rule for the translation can be written as t_-5,3(x, y). the rule for the translation can be written as t_3,-5(x, y). the rule for the translation can be written as (x, y) → (x + 3, y - 3). the rule for the translation can be written as (x, y) → (x - 3, y - 3). triangle abc has been translated 3 units to the right and 5 units down.

Explanation:

Step1: Observe x - coordinate change

To find the translation rule, look at the change in x - coordinates of corresponding points. For example, if we take point A. Let the coordinates of point A be \((x_1,y_1)\) and of \(A'\) be \((x_2,y_2)\). The x - coordinate of \(A\) is around \(- 2\) and of \(A'\) is around \(1\). The change in x is \(1-(-2)=3\), which means a shift of 3 units to the right.

Step2: Observe y - coordinate change

The y - coordinate of \(A\) is around \(3\) and of \(A'\) is around \(-2\). The change in y is \(-2 - 3=-5\), which means a shift of 5 units down.

Step3: Determine translation rule

The general form of a translation rule is \((x,y)\to(x + a,y + b)\), where \(a\) is the horizontal shift and \(b\) is the vertical shift. Here \(a = 3\) and \(b=-5\), so the rule is \((x,y)\to(x + 3,y-5)\) or \(T_{3,-5}(x,y)\)

Answer:

The rule for the translation can be written as \(T_{3,-5}(x,y)\); Triangle ABC has been translated 3 units to the right and 5 units down.