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.(1 point)
Responses

A′ (5, 10)
and B′ (−10, −5)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 10 comma negative 5 right parenthesis

A′ (5, 10)
and B′ (10, 5)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis 10 comma 5 right parenthesis

A′ (5, 10)
and B′ (−2, −1)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 2 comma negative 1 right parenthesis

A′ (1, 2)
and B′ (−10, −5)

Answer 1

To find the coordinates of points A' and B' after a dilation with a scale factor of 5 centered at the origin, you can use the formula for dilation:

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

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

Given:
- Point A(1, 2)
- Point B(−2, −1)
- Scale factor \(k = 5\)

Now, we can calculate the new coordinates.

**For point A(1, 2):**
\[
A' = (5 \cdot 1, 5 \cdot 2) = (5, 10)
\]

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

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

The correct response is:
**A′ (5, 10) and B′ (−10, −5)**.