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′ (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′ (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′ (−12, −8)

Answer 1

To find the coordinates of points A' and B' after a dilation, we can use the formula for dilation centered at the origin. The formula is:

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

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

In this case, the scale factor \( k = 4 \) and we have the following points:

- Point A (2, -5)
- Point B (−3, −2)

**Calculating A'**:

\[
A' = (4 \cdot 2, 4 \cdot (-5)) = (8, -20)
\]

**Calculating B'**:

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

Thus, the coordinates after the dilation are:

- \( A' (8, -20) \)
- \( B' (-12, -8) \)

So the correct response is:

**A′ (8, −20) and B′ (−12, −8)**.