Question

1. 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 + 3,y - 3)
b. (x - 3,y + 2)
c. (x + 3,y + 3)
d. (x + 2,y + 3)

Explanation:

Step1: Find change in x - coordinate

For point A, initial x - coordinate is 1 and final is 4. Change in x is \(4 - 1=3\). For point B, initial x - coordinate is 3 and final is 6. Change in x is \(6 - 3 = 3\). For point C, initial x - coordinate is 2 and final is 5. Change in x is \(5 - 2=3\).

Step2: Find change in y - coordinate

For point A, initial y - coordinate is 2 and final is 5. Change in y is \(5 - 2 = 3\). For point B, initial y - coordinate is 4 and final is 7. Change in y is \(7 - 4=3\). For point C, initial y - coordinate is 6 and final is 9. Change in y is \(9 - 6 = 3\).

Answer:

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