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′=
(
)
Remaining Attempts : 3

Answer 1

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

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

Applying this to 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 points after dilation are:

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

Thus, the final answers are:

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