Line AB

Question

A
B
contains point A (2, −5)
A

(
2
,

−
5
)
and point B (−3, −2)
B

(
−
3
,

−
2
)
. Find the coordinates of A′
A
′
and B′
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)
A
′

(
8
,

20
)
and B′ (12, 8)
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)
A
′

(
8
,

−
20
)
and B′ (−3, −2)
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)
A
′

(
8
,

−
20
)
and B′ (−12, −8)
B
′

(
−
12
,

−
8
)
upper A prime left parenthesis 8 comma negative 20 right parenthesis and upper B prime left parenthesis negative 12 comma negative 8 right parenthesis

A′ (2,−5)
A
′

(
2
,
−
5
)
and B′ (−12, −8)

Answer 1

To perform a dilation of points A(2, -5) and B(-3, -2) with a scale factor of 4 and a center point of dilation at the origin (0, 0), we use the following formula for dilation:

\[ A' = (kx, ky) \]

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

For point A(2, -5):

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

For point B(-3, -2):

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

Thus, the coordinates after the dilation are:

• \(A' (8, -20)\)
• \(B' (-12, -8)\)

The correct response is:

A′ (8, −20) and B′ (−12, −8).