Determine the scale factor used in the dilation of line segment AB, with a Center Point of dilation at the origin

Answer 1

To determine the scale factor used in the dilation of line segment AB with a center point at the origin, we need to know the coordinates of point A and point B.

Let's say the coordinates of point A are (x₁, y₁) and the coordinates of point B are (x₂, y₂).

The distance between the origin and point A is calculated using the distance formula:

d₁ = √((x₁ - 0)² + (y₁ - 0)²) = √(x₁² + y₁²)

Similarly, the distance between the origin and point B is:

d₂ = √((x₂ - 0)² + (y₂ - 0)²) = √(x₂² + y₂²)

The scale factor (k) is the ratio of the length of the dilated line segment over the length of the original line segment:

k = d₂ / d₁ = √(x₂² + y₂²) / √(x₁² + y₁²)

So, the scale factor used in the dilation of line segment AB with a center point at the origin is √(x₂² + y₂²) / √(x₁² + y₁²).