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 perform a dilation of triangle ABC with a scale factor of 7 from the origin (0,0), we'll apply the formula for dilation, which is given by:

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

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

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)**:

\[
C' = (7 \cdot (-2), 7 \cdot 5) = (-14, 35)
\]

Therefore, the coordinates of the points after dilation are:

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