Question

Line AB
contains point A (2, −5)
and point B (−3, −2)
. Find the coordinates of A′
and B′
after a dilation with a scale factor of 4 with a center point of dilation at the origin.(1 point)
Responses

A′ (2,−5)
and B′ (−12, −8)
upper A prime left parenthesis 2 comma negative 5 right parenthesis and upper B prime left parenthesis negative 12 comma negative 8 right parenthesis

A′ (8, 20)
and B′ (12, 8)
upper A prime left parenthesis 8 comma 20 right parenthesis and upper B prime left parenthesis 12 comma 8 right parenthesis

A′ (8, −20)
and B′ (−3, −2)
upper A prime left parenthesis 8 comma negative 20 right parenthesis and upper B prime left parenthesis negative 3 comma negative 2 right parenthesis

A′ (8, −20)
and B′ (−12, −8)

Answer 1

To find the coordinates of the points A′ and B′ after a dilation with a scale factor of 4 from the origin, we can apply the formula for dilation. The formula for dilating a point \((x, y)\) with a scale factor \(k\) from the origin is:

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

Given the coordinates of points A and B:

- Point A: (2, -5)
- Point B: (-3, -2)

We will compute the new coordinates for both points:

1. For point A (2, -5):
\[
A' = (4 \cdot 2, 4 \cdot -5) = (8, -20)
\]

2. For point B (-3, -2):
\[
B' = (4 \cdot -3, 4 \cdot -2) = (-12, -8)
\]

Therefore, the coordinates after the dilation are:
- A′ (8, -20)
- B′ (-12, -8)

The correct response is:
**A′ (8, −20) and B′ (−12, −8)**.