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.

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

Answer 1

To find the coordinates of points A′ and B′ after a dilation with a scale factor of 5 centered at the origin, we apply the dilation formula:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

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

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

2. 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 answer is:

**A′ (5, 10) and B′ (−10, −5)**