Question

Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A(3,7) and B(4,9) .(1 point) Responses A′(6,14) and B′(−4,3) upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis A′(6,14) and B′(8,18) upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis A′(−6,3) and B′(8,18) upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis A′(32,72) and B′(2,92)

Answer 1

To find the coordinates of points A and B after a dilation with a scale factor of 2, centered at the origin, we apply the dilation transformation to each coordinate.

The dilation transformation can be calculated using the formula:

\[
(x', y') = (kx, ky)
\]

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

Given:
- \(A(3, 7)\)
- \(B(4, 9)\)
- Scale factor \(k = 2\)

Let's calculate the new coordinates for point A:

\[
A' = (2 \cdot 3, 2 \cdot 7) = (6, 14)
\]

Now for point B:

\[
B' = (2 \cdot 4, 2 \cdot 9) = (8, 18)
\]

So after dilation, the coordinates are:
- \(A'(6, 14)\)
- \(B'(8, 18)\)

Therefore, the correct response is:
**A′(6,14) and B′(8,18)**