Square ABCD

Question

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 negative 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)

Answer 1

To find the coordinates of the vertices A′, B′, C′, and D′ after a dilation with a scale factor of 5 from the origin, we can use the formula for dilation:

\[ (x', y') = (k \cdot x, k \cdot y) \]

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

Given vertices:

• A(1, -3)
• B(4, -3)
• C(4, -1)
• D(1, -1)

Now calculate the dilated coordinates:

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

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

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

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

Final coordinates after dilation:

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

Thus, the correct response is:

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