Question

Select the coordinates A′
and B′
after dilation of the line segment AB
with a scale factor of 13
, centered at the origin where the endpoints are A(−6,3)
and B(−12,9)

Answer 1

To find the coordinates \(A'\) and \(B'\) after dilation of points \(A\) and \(B\) with a scale factor of 13 centered at the origin, we use the dilation transformation formula:

\[
(x, y) \rightarrow (kx, ky)
\]

where \(k\) is the scale factor.

Given:
- \(A(-6, 3)\)
- \(B(-12, 9)\)
- Scale factor \(k = 13\)

Now we apply the dilation to each point:

### For point \(A(-6, 3)\):
\[
A' = (13 \cdot -6, 13 \cdot 3) = (-78, 39)
\]

### For point \(B(-12, 9)\):
\[
B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117)
\]

Thus, the coordinates after dilation are:

- \(A'(-78, 39)\)
- \(B'(-156, 117)\)

In summary:
- \(A' = (-78, 39)\)
- \(B' = (-156, 117)\)