Question

Determine the scale factor used in the dilation of line segment AB, with a center point of dilation at the origin A(9,9) B(6,6) A(3,3) B(2,2)
-1/3
-3
1/3
3

Answer 1

To determine the scale factor used in the dilation of line segment AB, let's first identify the original coordinates of the points A and B and their dilated coordinates.

The original points are:
- A (9,9)
- B (6,6)

The dilated points are:
- A' (3,3)
- B' (2,2)

Next, we can find the scale factor \( k \) by using the formula for dilation, which is given by:

\[ A' = k \cdot A \]
\[ B' = k \cdot B \]

We can get the scale factor from the coordinates of either point A or point B.

For point A:

Using the coordinates of A:
- Original A: (9, 9)
- Dilated A': (3, 3)

We can find \( k \):
\[ 3 = k \cdot 9 \]

To find \( k \), we divide both sides by 9:
\[ k = \frac{3}{9} = \frac{1}{3} \]

Now checking for B:
- Original B: (6, 6)
- Dilated B': (2, 2)

Using B:
\[ 2 = k \cdot 6 \]

To find \( k \), we divide both sides by 6:
\[ k = \frac{2}{6} = \frac{1}{3} \]

Thus, the scale factor for the dilation is \( \frac{1}{3} \).

The answer is \( \frac{1}{3} \).