Use the image to answer the question.

Question

Quadrilateral A B C D is on a coordinate plane. The vertices are A at negative 1 comma 1, B at 1 comma 2, C at 3 comma 0, and D at 1 comma negative 1.

Identify the coordinates of the image of quadrilateral ABCD
after a dilation by a scale factor of 4 centered at the origin.

(2 points)
A′
(
), B′
(
), C′
(
), D′
(
)

Answer 1

To find the coordinates of the image of quadrilateral ABCD after a dilation by a scale factor of 4 centered at the origin, we multiply each coordinate of the vertices by the scale factor.

The original coordinates are:

• A (-1, 1)
• B (1, 2)
• C (3, 0)
• D (1, -1)

Now, applying the dilation:

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

2. For B (1, 2): \[ B' = (4 \cdot 1, 4 \cdot 2) = (4, 8) \]

3. For C (3, 0): \[ C' = (4 \cdot 3, 4 \cdot 0) = (12, 0) \]

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

Thus, the coordinates of the image of quadrilateral ABCD after dilation are:

• A′ (-4, 4)
• B′ (4, 8)
• C′ (12, 0)
• D′ (4, -4)

Final coordinates:

• A′ (-4, 4)
• B′ (4, 8)
• C′ (12, 0)
• D′ (4, -4)