Determine the scale factor used in the dilation of line AB , with a center point of dilation at the origin.
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 = â[(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' = â[(kx2 - kx1)^2 + (ky2 - ky1)^2]
= â[k^2(x2 - x1)^2 + k^2(y2 - y1)^2]
= kâ[(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.