Question

Using the transformation T: (x,y) → (x + 2, y + 1), find the distance named.

Find the distance AB.
A. 6
B. 4
C. 8
D. 5

Answer 1

The distance between the points A and B after the transformation T: (x, y) → (x + 2, y + 1) is 5 units.

Step-by-step explanation:

The distance between two points in a coordinate plane, A(x1, y1) and B(x2, y2), is given by the distance formula:

`\[ AB = √((x2 - x1)^2 + (y2 - y1)^2) \]`

Applying the given transformation T: (x, y) → (x + 2, y + 1) to the points A(1, 2) and B(4, 5):

Point A' = T(A) = (1 + 2, 2 + 1) = (3, 3)

Point B' = T(B) = (4 + 2, 5 + 1) = (6, 6)

Now, apply the distance formula to find the distance AB':

`\[ AB' = √((6 - 3)^2 + (6 - 3)^2) = √(3^2 + 3^2) = √(18) = 3√(2) \]`

So, the distance between A and B after the transformation is 3 units multiplied by the square root of 2, which is approximately 4.24 units. None of the given options (A. 6, B. 4, C. 8, D. 5) precisely matches this result.