Question

Find the dilation of
2
2 with center
(
0
,

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

(
8
,

9
)
A (8, 9)
B

(
−
2
,

−
3
)
B (−2, −3)



A
′
A
′

(
(

)
)



B
′
B
′

(
(

)
)

Answer 1

To find the dilation of points with a center (0, 0) and a scale factor of \( k = 2 \), we can use the formula for dilation:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

where \( (x, y) \) are the original coordinates of the points and \( (x', y') \) are the coordinates after dilation.

### For Point A (8, 9):

Using the dilation formula:

\[
A' = (2 \cdot 8, 2 \cdot 9) = (16, 18)
\]

### For Point B (-2, -3):

Using the dilation formula:

\[
B' = (2 \cdot -2, 2 \cdot -3) = (-4, -6)
\]

### Final Results:

- The dilated point \( A' \) is \( (16, 18) \)
- The dilated point \( B' \) is \( (-4, -6) \)

Thus, the results are:

\[
A' = (16, 18)
\]
\[
B' = (-4, -6)
\]