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′(−4,3)
𝐵
′
(
−
4
,
3
)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

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′(−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′(−18,9)
𝐴
′
(
−
18
,
9
)
and B′(−36

Answer 1

To find the coordinates $A^{\prime }$ and $B^{\prime }$ after a dilation of the line segment $AB$ with a scale factor of $\frac{1}{3}$, centered at the origin, we use the formula for dilation:

$$(x^{\prime },y^{\prime })=(kx,ky)$$

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

Given:

• Point $A(-6,3)$
• Point $B(-12,9)$

With a scale factor $k=\frac{1}{3}$:

For point $A^{\prime }$:

$$A^{\prime }=(-6\cdot \frac{1}{3},3\cdot \frac{1}{3})=(-2,1)$$

For point $B^{\prime }$:

$$B^{\prime }=(-12\cdot \frac{1}{3},9\cdot \frac{1}{3})=(-4,3)$$

Thus, the coordinates after dilation are:

$$A^{\prime }(-2,1)\text{and}{B}^{\prime }(-4,3)$$

So the correct choice is:

A′(−2,1) and B′(−4,3).