Question

Use the image to answer the question.

A coordinate plane with four quadrants shows the x-axis ranging from negative 11 to 5 in increments of 1 and the y-axis from 3 to negative 16 in increments of 1. Points upper A, upper B, upper A prime, and upper B prime are plotted on quadrant 3. The plotted points are as follows: Upper A is left parenthesis negative 1 comma negative 3 right parenthesis and upper B is left parenthesis negative 3 comma negative 5 right parenthesis. The points are joined by a line. Upper A prime is plotted as left parenthesis negative 3 comma negative 9 right parenthesis and upper B prime as left parenthesis negative 9 comma negative 15 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

[AI-generated answer — Bot GPT 3.5]

To find the scale factor used in the dilation of line segment AB, we need to compare the lengths of AB and A' B'.

Length of AB:
Using the distance formula, we can calculate the distance between points A and B:
AB = √((-3 - (-1))^2 + (-5 - (-3))^2) = √((-2)^2 + (-2)^2) = √8

Length of A' B':
Similarly, we can calculate the distance between points A' and B':
A' B' = √((-9 - (-3))^2 + (-15 - (-9))^2) = √((-6)^2 + (-6)^2) = √72

The scale factor can be obtained by dividing the length of A' B' by the length of AB:
Scale factor = A' B' / AB = √72 / √8 = √(72/8) = √9 = 3

Therefore, the scale factor used in the dilation of line segment AB is 3.