Rectangle ABCD

Question

A
B
C
D
has vertices point A(−5, 1)
A
(
−
5
,

1
)
, point B(−2, 1)
B
(
−
2
,

1
)
, point C(−2, 6)
C
(
−
2
,

6
)
, and point D(−5, 6)
D
(
−
5
,

6
)
. Find the coordinates of A′
A
′
, B′
B
′
, C′
C
′
, and D′
D
′
after a dilation with a scale factor of 3 and a center point of dilation at the origin.(1 point)
Responses

A′(−15, 3), B′(−6, 3), C′(−6, 18)
A
′
(
−
15
,

3
)
,

B
′
(
−
6
,

3
)
,

C
′
(
−
6
,

18
)
, and D′(−15, 18)
D
′
(
−
15
,

18
)
upper A prime left parenthesis negative 15 comma 3 right parenthesis comma upper B prime left parenthesis negative 6 comma 3 right parenthesis comma upper C prime left parenthesis negative 6 comma 18 right parenthesis , and upper D prime left parenthesis negative 15 comma 18 right parenthesis

A′(−15, 3), B′(−6, 3), C′(−6,−18)
A
′
(
−
15
,

3
)
,

B
′
(
−
6
,

3
)
,

C
′
(
−
6
,
−
18
)
, and D′(−15, 18)
D
′
(
−
15
,

18
)
upper A prime left parenthesis negative 15 comma 3 right parenthesis comma upper B prime left parenthesis negative 6 comma 3 right parenthesis comma upper C prime left parenthesis negative 6 comma negative 18 right parenthesis , and upper D prime left parenthesis negative 15 comma 18 right parenthesis

A′(15, 3), B′(−6, 3), C′(−6, 18)
A
′
(
15
,

3
)
,

B
′
(
−
6
,

3
)
,

C
′
(
−
6
,

18
)
, and D′(−15, 18)
D
′
(
−
15
,

18
)
upper A prime left parenthesis 15 comma 3 right parenthesis comma upper B prime left parenthesis negative 6 comma 3 right parenthesis comma upper C prime left parenthesis negative 6 comma 18 right parenthesis , and upper D prime left parenthesis negative 15 comma 18 right parenthesis

A′(−15, 3), B′(−6,−3), C′(−6, 18)
A
′
(
−
15
,

3
)
,

B
′
(
−
6
,
−
3
)
,

C
′
(
−
6
,

18
)
, and D′(−15, 18)

Answer 1

To find the coordinates of points \( A' \), \( B' \), \( C' \), and \( D' \) after a dilation with a scale factor of 3 centered at the origin, we need to multiply each coordinate of the original points by the scale factor.

The original coordinates are:

• \( A(-5, 1) \)
• \( B(-2, 1) \)
• \( C(-2, 6) \)
• \( D(-5, 6) \)

Now applying the dilation (scale factor of 3):

1. For point \( A' \): \[ A' = (3 \times -5, 3 \times 1) = (-15, 3) \]

2. For point \( B' \): \[ B' = (3 \times -2, 3 \times 1) = (-6, 3) \]

3. For point \( C' \): \[ C' = (3 \times -2, 3 \times 6) = (-6, 18) \]

4. For point \( D' \): \[ D' = (3 \times -5, 3 \times 6) = (-15, 18) \]

Combining these results, we have:

• \( A'(-15, 3) \)
• \( B'(-6, 3) \)
• \( C'(-6, 18) \)
• \( D'(-15, 18) \)

Thus, the correct response is: A′(−15, 3), B′(−6, 3), C′(−6, 18), and D′(−15, 18).