Question

Line AB
contains point A(−4, 1)
and point B (−1, 3)
. Find the coordinates of A′
and B′
after a dilation with a scale factor of 2 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 2 and with the center of dilation at the origin, we can use the formula for dilation:

\[
A' = (k \cdot x_A, k \cdot y_A)
\]
\[
B' = (k \cdot x_B, k \cdot y_B)
\]
where \( k \) is the scale factor, and \((x_A, y_A)\) and \((x_B, y_B)\) are the coordinates of points \( A \) and \( B \).

Given:
- Point \( A(-4, 1) \)
- Point \( B(-1, 3) \)
- Scale factor \( k = 2 \)

Now, we will apply the dilation to both points:

1. **For Point A:**
\[
A' = (2 \cdot -4, 2 \cdot 1) = (-8, 2)
\]

2. **For Point B:**
\[
B' = (2 \cdot -1, 2 \cdot 3) = (-2, 6)
\]

Thus, the coordinates after the dilation are:
- \( A'(-8, 2) \)
- \( B'(-2, 6) \)

Therefore, the coordinates of points \( A' \) and \( B' \) after the dilation are:
- \( A'(-8, 2) \)
- \( B'(-2, 6) \)