Question

3 multiple choice 10 points which statement is true about triangle abc and its translated image, abc? the rule for the translation can be written as (x,y)→(x + 3,y - 5). the rule for the translation can be written as (x,y)→(x - 3,y + 5). triangle abc has been translated 3 units to the left and 5 units up. triangle abc has been translated 3 units up and 5 to the left.

Explanation:

Step1: Observe x - coordinate change

Take a point, say A. A has coordinates (- 2,3). A' has coordinates (1, - 2). The change in x - coordinate is \(1-(-2)=3\), which means a shift of 3 units to the right (since \(x_{new}-x_{old}=3\)).

Step2: Observe y - coordinate change

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

Step3: Determine translation rule

The general rule for translation of a point \((x,y)\) to \((x',y')\) is \((x,y)\to(x + a,y + b)\), where \(a\) is the change in x and \(b\) is the change in y. Here \(a = 3\) and \(b=-5\), so the rule is \((x,y)\to(x + 3,y - 5)\).

Answer:

The rule for the translation can be written as \((x,y)\to(x + 3,y - 5)\).