Use the image to answer the question.

Question

Quadrilateral A B C D is on a coordinate plane. The vertices are A at negative 4 comma 2, B at 0 comma 6, C at 4 comma 6, and D at 8 comma 2.

Quadrilateral ABCD
has vertices at A(−4,2)
, B(0,6)
, C(4,6)
and D(8,2)
. Which graph shows the image of quadrilateral ABCD
after a dilation by a scale factor of 2 centered at the origin?

(1 point)
Responses

1.Quadrilateral A prime B prime C prime D prime is on a coordinate plane. The vertices are A prime at negative 8 comma 4, B prime at negative 2 comma 8, C prime at 2 comma 8, and D prime 6 comma 4.
Image with alt text: Quadrilateral A prime B prime C prime D prime is on a coordinate plane. The vertices are A prime at negative 8 comma 4, B prime at negative 2 comma 8, C prime at 2 comma 8, and D prime 6 comma 4.

2.Quadrilateral A prime B prime C prime D prime is on a coordinate plane. A prime at negative 8 comma 4, B prime at 0 comma 12, C prime at 8 comma 12, and D prime at 16 comma 4.
Image with alt text: Quadrilateral A prime B prime C prime D prime is on a coordinate plane. A prime at negative 8 comma 4, B prime at 0 comma 12, C prime at 8 comma 12, and D prime at 16 comma 4.

3.Quadrilateral A prime B prime C prime D prime is on a coordinate plane. The vertices are A prime at negative 8 comma 2, B prime at negative 2 comma 6, C prime at 2 comma 6, and D prime at 6 comma 2.
Image with alt text: Quadrilateral A prime B prime C prime D prime is on a coordinate plane. The vertices are A prime at negative 8 comma 2, B prime at negative 2 comma 6, C prime at 2 comma 6, and D prime at 6 comma 2.

4.Quadrilateral A prime B prime C prime D prime is on a coordinate plane. A prime at negative 2 comma 1, B prime at 0 comma 3, C prime at 2 comma 3, and D prime at 4 comma 1.

Answer 1

To find the image of quadrilateral ABCD after a dilation by a scale factor of 2 centered at the origin, we need to multiply the coordinates of each vertex by the scale factor (2).

The original vertices are:

• A(-4, 2)
• B(0, 6)
• C(4, 6)
• D(8, 2)

Let's calculate the coordinates after dilation:

1. For A(-4, 2):

   • A' = (-4 * 2, 2 * 2) = (-8, 4)

2. For B(0, 6):

   • B' = (0 * 2, 6 * 2) = (0, 12)

3. For C(4, 6):

   • C' = (4 * 2, 6 * 2) = (8, 12)

4. For D(8, 2):

   • D' = (8 * 2, 2 * 2) = (16, 4)

So, the coordinates of the dilated quadrilateral A'B'C'D' are:

• A'(-8, 4)
• B'(0, 12)
• C'(8, 12)
• D'(16, 4)

Now, let's compare these coordinates with the options given:

1. A' at (-8, 4), B' at (-2, 8), C' at (2, 8), D' at (6, 4).
2. A' at (-8, 4), B' at (0, 12), C' at (8, 12), D' at (16, 4).
3. A' at (-8, 2), B' at (-2, 6), C' at (2, 6), D' at (6, 2).
4. A' at (-2, 1), B' at (0, 3), C' at (2, 3), D' at (4, 1).

The correct response is:

2. Quadrilateral A'B'C'D' is on a coordinate plane. A' at (-8, 4), B' at (0, 12), C' at (8, 12), and D' at (16, 4).