Question

Describe the dilation of triangle ABC
, with a scale factor of 5 and a center point of dilation at the origin (0, 0)
.

Triangle A′B′C′
is 5 times smaller than triangle ABC
and is 5 times closer to the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times smaller than triangle upper A upper B upper C and is 5 times closer to the center point of dilation.

Triangle A′B′C′
is 5 times smaller than triangle ABC
and is 5 times as far from the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times smaller than triangle upper A upper B upper C and is 5 times as far from the center point of dilation.

Triangle A′B′C′
is 5 times as large as triangle ABC
and is 5 times as far from the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times as large as triangle upper A upper B upper C and is 5 times as far from the center point of dilation.

Triangle A′B′C′
is 5 times as large as triangle ABC
and is 5 times closer to the center point of dilation

Answer 1

To describe the dilation of triangle ABC with a scale factor of 5 and a center of dilation at the origin (0, 0), we need to understand what dilation means in geometry.

**Dilation** is a transformation that alters the size of a figure without changing its shape. When a figure is dilated by a scale factor \( k \) from a center point, each point of the figure moves away from (or towards, if \( k < 1 \)) the center of dilation by a distance that is multiplied by \( k \).

In this case:

- **Scale Factor**: \( k = 5 \) (which means the new figure will be 5 times larger)
- **Center of Dilation**: \( (0, 0) \)

When triangle ABC is dilated by a scale factor of 5 from the origin (0, 0), each vertex of the triangle will be moved outward from the origin. If the original vertices of triangle ABC are \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \), the coordinates of the new vertices \( A', B', C' \) of triangle A'B'C' after dilation will be calculated by the following formula:

- \( A' = (5 \cdot x_1, 5 \cdot y_1) \)
- \( B' = (5 \cdot x_2, 5 \cdot y_2) \)
- \( C' = (5 \cdot x_3, 5 \cdot y_3) \)

### Interpretation of Dilation Results
1. **Triangle A'B'C' is 5 times larger than triangle ABC**: This is a direct consequence of the scale factor of 5. Each side of triangle A'B'C' is 5 times the corresponding side of triangle ABC.

2. **Triangle A'B'C' is 5 times as far from the center of dilation (the origin)**: Since the scaling factor is 5, each point of the triangle moves away from the origin to a distance that is multiplied by 5.

### Conclusion
Given your options:

- Triangle A'B'C' is 5 times larger than triangle ABC and is 5 times as far from the center point of dilation.

This statement accurately describes the outcome of the dilation transformation given the specified parameters (a scale factor of 5 and center of dilation at the origin).