Question

what is the rule for this translation? (x, y) --> (x+6, y-4) (x, y) --> (x-4, y-6) (x, y) --> (x+5, y-3)

Explanation:

Step1: Observe x - coordinate change

Pick a point on the original triangle, say \(T\). Its \(x\) - coordinate changes from \(x=-2\) to \(x = 4\) in the translated triangle \(T'\). The change in \(x\) is \(4-(-2)=6\), so \(x\) - coordinate of each point in the original figure is increased by 6.

Step2: Observe y - coordinate change

The \(y\) - coordinate of point \(T\) changes from \(y = 2\) to \(y=-2\) in the translated triangle \(T'\). The change in \(y\) is \(-2 - 2=-4\), so \(y\) - coordinate of each point in the original figure is decreased by 4.

Answer:

\((x,y)\to(x + 6,y-4)\)