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Find the dilation of

0.25
0.25 with center
(
0
,

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

(
7
,

−
4
)
A (7, −4)
𝐵

(
−
8
,

−
2
)
B (−8, −2)

𝐴
′
A
′

(
(

)
)

𝐵
′
B
′

(
(

)
)

1 answer

To find the dilation of points \( A(7, -4) \) and \( B(-8, -2) \) with center \( (0, 0) \) and a scale factor of \( 0.25 \), we can use the formula for dilation:

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

For point \( A(7, -4) \):

  1. Calculate the new coordinates: \[ A' = (0.25 \cdot 7, 0.25 \cdot -4) \] \[ A' = (1.75, -1) \]

For point \( B(-8, -2) \):

  1. Calculate the new coordinates: \[ B' = (0.25 \cdot -8, 0.25 \cdot -2) \] \[ B' = (-2, -0.5) \]

Final Results:

  • The dilated point \( A' \) is \( (1.75, -1) \).
  • The dilated point \( B' \) is \( (-2, -0.5) \).

Thus, the coordinates are:

  • \( A' (1.75, -1) \)
  • \( B' (-2, -0.5) \)