Final answer:
To find the distance using the given transformation T: (x, y) → (x + 2, y + 1), we can use the formula for distance between two points in a coordinate plane.
Step-by-step explanation:
To find the distance using the given transformation T: (x, y) → (x + 2, y + 1), we can use the formula for distance between two points in a coordinate plane. The distance between two points (x1, y1) and (x2, y2) is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the initial point is (x, y) and the transformed point is (x + 2, y + 1). Plugging in the values, the distance is:
distance = sqrt((x + 2 - x)^2 + (y + 1 - y)^2)
= sqrt(2^2 + 1^2)
= sqrt(4 + 1)
= sqrt(5)
Therefore, the distance is sqrt(5), which is approximately 2.236. None of the given options in the question match this distance, so none of them is the correct answer.
The straight-line distance between two points, (x1, y1) and (x2, y2), in a two-dimensional space is given by the formula d = √((x2 - x1)² + (y2 - y1)²). For example, if you started at point A (2,3) and applied transformation T, your new point B would be (2+2, 3+1) or (4, 4). The distance between A and B would then be √((4 - 2)² + (4 - 3)²) = √(4 + 1) = √5 which is approximately 2.24 units.