Question

(2, 5) is the image of (7, 11) under a translation, T. Which of the following is TRUE?

Option 1: T(x, y) = (x+7, y+11)
Option 2: T(x, y) = (x+2, y+5)
Option 3: T(x, y) = (x+5, y+6)
Option 4: T(x, y) = (x-5, y-6)

Answer 1

The correct translation that maps (7, 11) to (2, 5) is Option 4: T(x, y) = (x-5, y-6).

Step-by-step explanation:

In a translation, the image of a point (x, y) is obtained by adding the same amount to both the x-coordinate and the y-coordinate. So, we need to find which option correctly represents the translation that maps (7, 11) to (2, 5).

Option 1: T(x, y) = (x+7, y+11)

Option 2: T(x, y) = (x+2, y+5)

Option 3: T(x, y) = (x+5, y+6)

Option 4: T(x, y) = (x-5, y-6)

To check which option is correct, we can subtract 7 from the x-coordinate and 11 from the y-coordinate of (2, 5).

2 - 7 = -5

5 - 11 = -6

The correct translation is Option 4: T(x, y) = (x-5, y-6).