Question

Use the image to answer the question.

A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows and 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. A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows and ranging from 15 to negative 4 in 1 unit increments. 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 joined by a line that extends beyond the points and is capped with arrows at both ends. 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 joined by a line that extends beyond the points and is capped with arrows at both ends.

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

(1 point)
Responses

−3
negative 3

3
3

−13
negative Start Fraction 1 over 3 End Fraction

13
Start Fraction 1 over 3 End Fraction
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the scale factor, we can compare the distances between the points on the original line AB and the corresponding points on the dilated line A'B'.

The distance between A and B on the original line AB is 6-9 = -3 units.

The distance between A' and B' on the dilated line A'B' is 2-3 = -1 unit.

Therefore, the scale factor used in the dilation of line AB is equal to the ratio of the distances: (-1)/(-3) = 1/3.

So, the correct answer is: Start Fraction 1 over 3 End Fraction.