Answer: The value of a is 2 and the value of b is 3.
Explanation:
Given : △CDE maps to △STU with the transformations (x, y) → (x − 2, y − 2) →(3x, 3y)
The first transformation is a translation ,so there will be no change in the length of the sides ∵ translation is a rigid motion.
The second transformation is a dilation ,so there will be a change in the length of the sides by scale factor of 3. ∵ dilation is not a rigid motion.
Basically , by combining both transformation:
Length of Side in △STU = 3 x (Corresponding side in △CDE )
⇒ ST = 3CD and TU = 3 DE
If CD = a + 1, DE = 2a − 1, ST = 2b + 3 and TU = b + 6 , then
2b + 3=3(a + 1) and b + 6 = 3(2a − 1)
⇒ 2b + 3=3a+3 and b + 6 = 6a-3
⇒ 3a-2b=0 (i) and b = 6a-9 (ii)
Put value of b from (ii) in (i) , we get
3a-2(6a-9)=0
⇒ 3a-12a+18=0
⇒ -9a=-18
⇒ a= 2
Put value of a in (ii) , we get
b= 6(2)-9
=12-9=3
Hence, the value of a is 2 and the value of b is 3.