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: Analyze horizontal translation

To find the horizontal translation, compare the x - coordinates of corresponding points. For example, if we take point B(-1,1) and B'(2, - 4), the change in the x - coordinate is \(2-(-1)=3\). This means the figure is translated 3 units to the right.

Step2: Analyze vertical translation

Compare the y - coordinates of corresponding points. Using B(-1,1) and B'(2,-4), the change in the y - coordinate is \(-4 - 1=-5\). This means the figure is translated 5 units down.

Step3: Determine the translation rule

The general rule for a translation is \((x,y)\to(x + a,y + b)\), where \(a\) is the horizontal change and \(b\) is the vertical change. 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.