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

Question

(1 point)

Answer 1

To determine the scale factor, we need to compare the lengths of the original line segment AB and the dilated line segment AB'.

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

The length of the original line segment AB can be found using the distance formula:

AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's say the coordinates of the dilated points are A' = (kx1, ky1) and B' = (kx2, ky2) where k is the scale factor.

The length of the dilated line segment AB' can then be found using the distance formula:

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

We know that the scale factor k is the same for both line segments, so AB' = k * AB.

Therefore, the scale factor used in the dilation of line segment AB is equal to the ratio of the length of the dilated line segment to the length of the original line segment:

k = AB' / AB

Answer 2

what numbered answer

Answer 3

The scale factor used in the dilation of line segment AB with a center point of dilation at the origin is:

(3) k = AB' / AB