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

−13
negative Start Fraction 1 over 3 End Fraction

3
3

−3

Answer 1

To determine the scale factor used in the dilation of line segment AB with a center of dilation at the origin, we first need to identify the coordinates of points A and B, as well as their corresponding points after dilation, A' and B'.

Given:

- Point A: (9, 9)
- Point B: (6, 6)
- Point A': (3, 3)
- Point B': (2, 2)

Now, we can calculate the scale factor for each point. The scale factor (k) for a dilation from a point (x, y) to a point (x', y') can be calculated using the formula:
\[ k = \frac{x'}{x} \]
Since the dilation is centered at the origin (0, 0), we can find the scale factors for points A and A':

**For Point A:**
\[ k_A = \frac{3}{9} = \frac{1}{3} \]

**For Point B:**
\[ k_B = \frac{2}{6} = \frac{1}{3} \]

Both points A and B have the same scale factor of \( \frac{1}{3} \).

Thus, the scale factor used in the dilation of line segment AB is \( \frac{1}{3} \).

Final answer:
**Start Fraction 1 over 3 End Fraction**