Select the coordinates A′

Question

A
′
and B′
B
′
after dilation of the line segment AB
A
B
with a scale factor of 13
1
3
, centered at the origin where the endpoints are A(−6,3)
A
(
−
6
,
3
)
and B(−12,9)
B
(
−
12
,
9
)
.(1 point)
Responses

A′(−2,1)
A
′
(
−
2
,
1
)
and B′(−12,9)
B
′
(
−
12
,
9
)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 12 comma 9 right parenthesis

A′(−18,9)
A
′
(
−
18
,
9
)
and B′(−36,27)
B
′
(
−
36
,
27
)
upper A prime left parenthesis negative 18 comma 9 right parenthesis and upper B prime left parenthesis negative 36 comma 27 right parenthesis

A′(−6,3)
A
′
(
−
6
,
3
)
and B′(−4,3)
B
′
(
−
4
,
3
)
upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

A′(−2,1)
A
′
(
−
2
,
1
)
and B′(−4,3)

Answer 1

To perform a dilation of a point \((x, y)\) centered at the origin with a scale factor of \(k\), you apply the transformation:

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

Given the coordinates of the points \(A(-6, 3)\) and \(B(-12, 9)\) and the scale factor of \(k = \frac{1}{3}\):

1. For point \(A\): \[ A' = \left(-6 \cdot \frac{1}{3}, 3 \cdot \frac{1}{3}\right) = \left(-2, 1\right) \]

2. For point \(B\): \[ B' = \left(-12 \cdot \frac{1}{3}, 9 \cdot \frac{1}{3}\right) = \left(-4, 3\right) \]

Thus, the coordinates after dilation are:

\[ A'(-2, 1) \quad \text{and} \quad B'(-4, 3) \]

The correct response is:

A′(−2,1) and B′(−4,3).