Answer: The translation rule that maps point D ( 7 , − 3 ) onto point D ' ( 2 , 5 )
is (x , y) → (x - 5 , y + 8)
Step-by-step explanation:
Let us revise the translation
If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)
If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)
If the point (x , y) translated vertically up by k units then its image is (x , y + k)
If the point (x , y) translated vertically down by k units then its image is (x , y - k)
(x , y) → (x ± h , y ± k) the right arrow symbol used to show the
translation from a point to its image
Example:
∵ P (0 , 0) → P' (1 , 2)
∴ The rule is (x , y) → (x + 1 , y + 2)
Let us find the translation rule that maps point D ( 7 , − 3 ) onto
point D' (2 , 5)
∵ Point (x , y) = (7 , -3)
∵ Its image after translation (x + h , y + k) = (2 , 5)
∴ x + h = 2
∵ x = 7
∴ 7 + h = 2
- Subtract 7 from both sides
∴ h = -5
∵ y + k = 5
∵ y = -3
∴ -3 + k = 5
- Add 3 to both sides
∴ k = 8
∴ The rule of translation is (x , y) → (x - 5 , y + 8)
The translation rule that maps point D ( 7 , − 3 ) onto point D ' ( 2 , 5 )
is (x , y) → (x - 5 , y + 8)
and height determined by the vertical distance between the upper blue curve and the lower orange curve for any given 
.