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: Find coordinates of points

Let's assume \(A(-1,3)\), \(B(-1,1)\), \(C(3,1)\) and \(A'(2,0)\), \(B'(2, - 2)\), \(C'(6,-2)\)

Step2: Calculate translation

For \(x\) - coordinate: \(2-(-1)=3\) (right - shift if positive). For \(y\) - coordinate: \(0 - 3=-3\) (down - shift if negative). The translation rule is \((x,y)\to(x + 3,y-3)\) which is equivalent to \(T_{3,-3}(x,y)\)

Answer:

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