Question

Find the dilation of
0.25
0.25 with center
(
0
,

0
)
(0, 0) for the following points if
𝐴

(
−
6
,

−
5
)
A (−6, −5)
𝐵

(
−
3
,

5
)
B (−3, 5)



𝐴
′
A
′

(
(

)
)



𝐵
′
B
′

(
(

)
)

Answer 1

To find the dilated points \( A' \) and \( B' \) of the points \( A(-6, -5) \) and \( B(-3, 5) \) with a dilation factor of \( 0.25 \) and centered at \( (0, 0) \), we can use the formula for dilation:

\[
A' = \left( k \cdot x, k \cdot y \right)
\]
where \( k \) is the dilation factor and \( (x, y) \) are the coordinates of the original point.

### Dilation of Point A

For point \( A(-6, -5) \):
- \( x = -6 \)
- \( y = -5 \)
- \( k = 0.25 \)

Calculating the dilated coordinates:

\[
A' = \left( 0.25 \cdot (-6), 0.25 \cdot (-5) \right) = \left( -1.5, -1.25 \right)
\]

### Dilation of Point B

For point \( B(-3, 5) \):
- \( x = -3 \)
- \( y = 5 \)
- \( k = 0.25 \)

Calculating the dilated coordinates:

\[
B' = \left( 0.25 \cdot (-3), 0.25 \cdot 5 \right) = \left( -0.75, 1.25 \right)
\]

### Final Results

Thus, the dilated points are:

\[
A' = (-1.5, -1.25)
\]
\[
B' = (-0.75, 1.25)
\]