Question

Find the dilation of
0.5
0.5 with center
(
0
,

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

(
−
3
,

8
)
A (−3, 8)
B

(
9
,

1
)
B (9, 1)



A
′
A
′

(
(

)
)



B
′
B
′

(
(

)
)

Answer 1

To find the dilation of points A and B with a scale factor of 0.5 and center at (0, 0), we use the dilation formula:

\[
A' = (kx, ky)
\]

where \( (x, y) \) is the original point, \( k \) is the scale factor, and \( (A', B') \) is the resulting point after dilation.

### For point A (−3, 8):

1. **Calculate the dilated x-coordinate:**

\[
A'_x = k \cdot A_x = 0.5 \cdot (-3) = -1.5
\]

2. **Calculate the dilated y-coordinate:**

\[
A'_y = k \cdot A_y = 0.5 \cdot 8 = 4
\]

Thus, point \( A' \) after dilation:

\[
A' = (-1.5, 4)
\]

### For point B (9, 1):

1. **Calculate the dilated x-coordinate:**

\[
B'_x = k \cdot B_x = 0.5 \cdot 9 = 4.5
\]

2. **Calculate the dilated y-coordinate:**

\[
B'_y = k \cdot B_y = 0.5 \cdot 1 = 0.5
\]

Thus, point \( B' \) after dilation:

\[
B' = (4.5, 0.5)
\]

### Final Results:

- A′ = \( (-1.5, 4) \)
- B′ = \( (4.5, 0.5) \)