Question

Line AB
contains point A(1, 2)
and point B (−2, −1)
. Find the coordinates of A′
and B′
after a dilation with a scale factor of 5 with a center point of dilation at the origin.

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after a dilation with a scale factor of 5 and a center of dilation at the origin, we can use the formula for dilation:

\[
A' = (kx, ky)
\]

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

### Step 1: Dilation of point A(1, 2)

For point \( A(1, 2) \):
- Coordinates after dilation:
\[
A' = (5 \cdot 1, 5 \cdot 2) = (5, 10)
\]

### Step 2: Dilation of point B(−2, −1)

For point \( B(−2, −1) \):
- Coordinates after dilation:
\[
B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5)
\]

### Conclusion

The coordinates after the dilation are:
- \( A' = (5, 10) \)
- \( B' = (-10, -5) \)