Determine the scale factor used in the dilation of line AB , with a center point of dilation at the origin.

Answer 1

To determine the scale factor used in the dilation of line AB with a center point at the origin, we need to compare the lengths of the original line AB and the dilated line AB'.

Let's say the coordinates of point A are (x1, y1) and the coordinates of point B are (x2, y2). The distance formula between two points (x1, y1) and (x2, y2) is given by:

AB = √[(x2 - x1)^2 + (y2 - y1)^2]

Now, let's say the coordinates of the dilated points A' and B' are (kx1, ky1) and (kx2, ky2) respectively, where k is the scale factor. The distance formula between points A' and B' is:

AB' = √[(kx2 - kx1)^2 + (ky2 - ky1)^2]
= √[k^2(x2 - x1)^2 + k^2(y2 - y1)^2]
= k√[(x2 - x1)^2 + (y2 - y1)^2]
= k * AB

Therefore, the scale factor used in the dilation of line AB with a center point at the origin is k.