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)

Answer 1

To find the coordinates of the points A′, B′, and C′ after dilation with a scale factor of 7 and the center of dilation at the origin (0,0), we can use the following formula for dilation:

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

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

Given the scale factor \( k = 7 \), we can find:

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

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

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

Thus, the coordinates of the points after dilation are:
- \( A' (14, 7) \)
- \( B' (28, 21) \)
- \( C' (-14, 35) \)