Question

a triangle has vertices a(1,2), b(3,4), and c(2,6). after a transformation, the vertices become a(4,5), b(6,7), and c(5,9). what is the translation rule? a. (x + 2,y + 3) b. (x + 3,y + 3) c. (x + 3,y - 3) d. (x - 3,y + 2)

Explanation:

Step1: Analyze x - coordinate change

For point A: Initial x - coordinate is 1, final is 4. Change is \(4 - 1=3\). For point B: Initial x - coordinate is 3, final is 6. Change is \(6 - 3 = 3\). For point C: Initial x - coordinate is 2, final is 5. Change is \(5 - 2=3\). So the change in x - coordinate is \(x
ightarrow x + 3\).

Step2: Analyze y - coordinate change

For point A: Initial y - coordinate is 2, final is 5. Change is \(5 - 2 = 3\). For point B: Initial y - coordinate is 4, final is 7. Change is \(7 - 4=3\). For point C: Initial y - coordinate is 6, final is 9. Change is \(9 - 6 = 3\). So the change in y - coordinate is \(y
ightarrow y + 3\).

Answer:

b. \((x + 3,y + 3)\)