Question

Use the image to answer the question.

A coordinate plane with four quadrants shows an x axis capped with arrows ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows ranging from 15 to negative 4 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted in quadrant 1. Point upper A is plotted as left parenthesis 9 comma 9 right parenthesis and point upper B is plotted as left parenthesis 6 comma 6 right parenthesis. The points are plotted on a line segment. Point upper A prime is plotted as left parenthesis 3 comma 3 right parenthesis and upper B prime is plotted as left parenthesis 2 comma 2 right parenthesis. The points are plotted on a line segment.

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

13
Start Fraction 1 over 3 End Fraction
3
3
−3
negative 3
−13
negative Start Fraction 1 over 3 End Fraction

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

The original line segment AB has a length of 3 units (distance from point A to point B).

The dilated line segment A' B' has a length of 1 unit (distance from point A' to point B').

To find the scale factor, we divide the length of the dilated line segment by the length of the original line segment:

1 / 3 = 1/3

Therefore, the scale factor used in the dilation of line segment AB with a center point of dilation at the origin is 1/3.