Question

Rectangle ABCD has vertices A(1, 1) , B(1, 7) , C(3, 7) , and D(3, 1) . A dilation with a scale factor of 0.4 and centered at the origin is applied to the rectangle.

Which vertex in the dilated image has coordinates of (0.4, 2.8) ?

Responses

A′
A prime

B′
B prime

C′
C prime

D′

Answer 1

To find out which vertex of rectangle ABCD corresponds to the dilated coordinates (0.4, 2.8), we first need to apply the dilation to each vertex of the rectangle.

The original vertices of rectangle ABCD are:
- A(1, 1)
- B(1, 7)
- C(3, 7)
- D(3, 1)

A dilation with a scale factor of 0.4 centered at the origin transforms each vertex (x, y) to (0.4x, 0.4y).

Now let's calculate the dilated coordinates for each vertex:

1. For A(1, 1):
- A' = (0.4 * 1, 0.4 * 1) = (0.4, 0.4)

2. For B(1, 7):
- B' = (0.4 * 1, 0.4 * 7) = (0.4, 2.8)

3. For C(3, 7):
- C' = (0.4 * 3, 0.4 * 7) = (1.2, 2.8)

4. For D(3, 1):
- D' = (0.4 * 3, 0.4 * 1) = (1.2, 0.4)

Looking at the dilated coordinates, we find that the vertex B' has coordinates (0.4, 2.8).

Therefore, the vertex in the dilated image that has coordinates (0.4, 2.8) is:
**B′ (B prime)**.