Question

Question
Square ABCD
has vertices point A(1, −3)
, point B(4, −3)
, point C(4, −1)
, and point D(1, −1)
. Find the coordinates of A′
, B′
, C′
, and D′
after a dilation with a scale factor of 5 and a center point of dilation at the origin.(1 point)
Responses

A′(5, −15)
, B′ (−20, −15)
, C′ (20, −5)
, and D′(5, −5)
upper A prime left parenthesis 5 comma negative 15 right parenthesis , upper B prime left parenthesis negative 20 comma negative 15 right parenthesis , upper C prime left parenthesis 20 comma negative 5 right parenthesis , and upper D prime left parenthesis 5 comma negative 5 right parenthesis

A′(5, −15)
, B′ (20, −15)
, C′ (20, −5)
, and D′(5, −5)
upper A prime left parenthesis 5 comma negative 15 right parenthesis , upper B prime left parenthesis 20 comma negative 15 right parenthesis , upper C prime left parenthesis 20 comma negative 5 right parenthesis , and upper D prime left parenthesis 5 comma negative 5 right parenthesis

A′(5, −15)
, B′ (20, −15)
, C′ (20, −5)
, and D′(−5, −5)
upper A prime left parenthesis 5 comma negative 15 right parenthesis , upper B prime left parenthesis 20 comma negative 15 right parenthesis , upper C prime left parenthesis 20 comma negative 5 right parenthesis , and upper D prime left parenthesis negative 5 comma negative 5 right parenthesis

A′(−5, −15)
, B′ (20, −15)
, C′ (20, −5)
, and D′(5, −5)

Answer 1

To find the coordinates of the dilated points A′, B′, C′, and D′ after performing a dilation with a scale factor of 5 from the origin (0, 0), we use the dilation formula:

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

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

For our square:

1. Point A(1, −3):
\[
A' = (5 \cdot 1, 5 \cdot -3) = (5, -15)
\]

2. Point B(4, −3):
\[
B' = (5 \cdot 4, 5 \cdot -3) = (20, -15)
\]

3. Point C(4, −1):
\[
C' = (5 \cdot 4, 5 \cdot -1) = (20, -5)
\]

4. Point D(1, −1):
\[
D' = (5 \cdot 1, 5 \cdot -1) = (5, -5)
\]

Now, we can list the dilated coordinates:
- A′(5, −15)
- B′(20, −15)
- C′(20, −5)
- D′(5, −5)

Thus, the correct response for the coordinates after dilation is:

A′(5, −15), B′(20, −15), C′(20, −5), and D′(5, −5)