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 t3, - 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 \(A'(2, - 2)\), \(B'(2,-4)\), \(C'(6,-4)\)

Step2: Calculate translation rule

For \(x\)-coordinate: \(x\) of \(A\) is \(-1\), \(x\) of \(A'\) is \(2\), \(2-(-1)=3\)
For \(y\)-coordinate: \(y\) of \(A\) is \(3\), \(y\) of \(A'\) is \(-2\), \(-2 - 3=-5\)
The translation rule is \((x,y)\to(x + 3,y-5)\) which can also be written as \(T_{3,-5}(x,y)\)
Another way: moving 3 units right ( \(x\) - coordinate change \(+3\)) and 5 units down (\(y\) - coordinate change \(-5\))

Answer:

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