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

Observe the x - coordinates of corresponding points. For example, if we consider point A and A', we can see that the x - coordinate of each point in the original triangle is increased by 3 to get the x - coordinate of the corresponding point in the translated triangle. This means a horizontal shift of 3 units to the right.

Step2: Analyze vertical translation

Look at the y - coordinates of corresponding points. The y - coordinate of each point in the original triangle is decreased by 3 to get the y - coordinate of the corresponding point in the translated triangle. This means a vertical shift of 3 units down.

Step3: Determine translation rule

The general rule for translation is \((x,y)\to(x + a,y + b)\), where \(a\) is the horizontal shift and \(b\) is the vertical shift. Here \(a = 3\) (right - shift) and \(b=- 3\) (down - shift), so the rule is \((x,y)\to(x + 3,y - 3)\).

Answer:

The rule for the translation can be written as \((x,y)\to(x + 3,y - 3)\)