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 - 3, - 3(x, y). the rule for the translation can be written as t3 - 3(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 3 units down.

Explanation:

Step1: Observe the translation

To find the translation rule, we look at the change in the x - and y - coordinates of a point on the original triangle (blue) and its corresponding point on the translated triangle (red).

Step2: Determine the change in x - coordinate

Pick a vertex, say the left - most vertex of the blue triangle. Its x - coordinate changes from \(x_1=-2\) to \(x_2 = 1\) in the red triangle. The change in x is \(1-(-2)=3\) (a shift of 3 units to the right).

Step3: Determine the change in y - coordinate

The y - coordinate of the same vertex changes from \(y_1 = 3\) to \(y_2=-2\) in the red triangle. The change in y is \(-2 - 3=-5\) (a shift of 5 units down).

Step4: Write the translation rule

The general rule for a translation is \((x,y)\to(x + a,y + b)\), where \(a\) is the change in the x - coordinate and \(b\) is the change in the y - coordinate. Here \(a = 3\) and \(b=-5\), so the rule is \((x,y)\to(x + 3,y-5)\) which can also be written as \(T_{3,-5}(x,y)\)

Answer:

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