Question

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Dilations & Figures Practice
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Question
Triangle ABC
has vertices point A(2,1)
, point B(4,3)
, and point C(−2,5)
. Find the coordinates of A′
, B′
, and C′
after a dilation with a scale factor of 7 and a center point of dilation at the origin (0,0)
.(2 points)
A′=
(
,
)
B′=
(
,
)
C′=
(
,
)

Answer 1

To find the coordinates of the points \( A' \), \( B' \), and \( C' \) after a dilation with a scale factor of 7 and a center at the origin (0,0), you can apply the dilation formula:

\[
(x', y') = (kx, ky)
\]

where \( (x, y) \) are the original coordinates of the point, \( k \) is the scale factor, and \( (x', y') \) are the coordinates of the dilated point.

Given the scale factor \( k = 7 \), we can calculate the new coordinates for each vertex:

1. For point \( A(2,1) \):
\[
A' = (7 \cdot 2, 7 \cdot 1) = (14, 7)
\]

2. For point \( B(4,3) \):
\[
B' = (7 \cdot 4, 7 \cdot 3) = (28, 21)
\]

3. For point \( C(-2,5) \):
\[
C' = (7 \cdot -2, 7 \cdot 5) = (-14, 35)
\]

So the coordinates of the dilated points are:

- \( A' = (14, 7) \)
- \( B' = (28, 21) \)
- \( C' = (-14, 35) \)

Final answer:
- \( A' = (14, 7) \)
- \( B' = (28, 21) \)
- \( C' = (-14, 35) \)