Question

If T1(x,y)=(x+3, y-4) and T2 (x,y)=. (x+1, y+7), what is the rule for thetranslation T1 followed by T2? T (x,y)=(x+?, y+?)

Answer 1

Answer: T(x,y) = (x+4, y+3)

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When we apply the rule T1, we shift the point 3 units to the right as x+3 indicates. Then when T2 happens, we shift another 1 unit to the right due to the x+1. Overall, the point will shift 4 units to the right (3+1 = 4) after we apply T1 and then T2. The order of the translations doesn't matter. Therefore the x part of the rule is x+4

For the y shifts, T1 moves the point down 4 units and T2 moves the point up 7 units. The net of this is 3 units up because 7+(-4) = 3. Therefore the y portion will be y+3

Overall, we combine the two pieces to get this complete transformation: T(x,y) = (x+4, y+3) telling us to move the point 4 units to the right and 3 units up.