Determine the end points of the translated line:

Let a line AB whose position vectors of end points are

 [A] = [1, 2]      [B] = [3, 4]

The translations in x and y directions are following

[T_x, T_y] = [2, 3]

Determine the end points of the translated line.

Solution

 [ x₁ , y₁ ] = [1, 2] [ x₂ , y₂ ] = [3, 4]

x₁′ = x₁  + T_x = 1 + 2 = 3 x₂′ = x₂ + T_x = 3 + 2 = 5

y₁′ = y₁  + T_y = 2 + 3 = 5 y₂′ = y₂ + T_y = 4 + 3 = 7

OL : Original Line

TL : Transformed Line

Figure

∴ The point A & B have been translated respectively to [3, 5] and [5, 7].