Question

A coordinate plane with four quadrants shows x-axis ranging from negative 5 to 12 in increments of 1 and the y-axis from 17 to negative 4 in increments of 1. Points upper A, upper B, upper A prime, and upper B prime are plotted on quadrant 1. The plotted points are as follows: Upper A is left parenthesis 2 comma 3 right parenthesis and upper B is left parenthesis 4 comma 1 right parenthesis. The points are joined by a line. Upper A prime is plotted as left parenthesis 6 comma 9 right parenthesis and upper B prime as left parenthesis 12 comma 3 right parenthesis. The points are joined by a line.
Determine the scale factor used in the dilation of line segment AB
, centered at the origin.

Answer 1

Scale factor k = 3.

Reason: A = (2,3) → A' = (6,9) and B = (4,1) → B' = (12,3). For a dilation about the origin, multiply coordinates by k, and 6/2 = 9/3 = 12/4 = 3.