Question

In the image, triangle ABC is dilated with reference to the origin to create triangle A'B'C'. What is the magnitude of dilation?

(1 point)
Triangle ABC is dilated using a magnitude of
, which results in triangle A'B'C'.

Answer 1

To find the magnitude of dilation for triangle ABC to triangle A'B'C', you need to compare the distance from the origin to the vertices of triangle ABC with the distance from the origin to the corresponding vertices of triangle A'B'C'.

If the coordinates of the vertices of triangle ABC are \(A(x_1, y_1)\), \(B(x_2, y_2)\), and \(C(x_3, y_3)\), and the coordinates of the vertices of triangle A'B'C' are \(A'(kx_1, ky_1)\), \(B'(kx_2, ky_2)\), and \(C'(kx_3, ky_3)\), where \(k\) is the dilation factor, then the dilation can be expressed as:

1. Measure the distance from the origin to point A in triangle ABC:
\[
d_{ABC} = \sqrt{x_1^2 + y_1^2}
\]

2. Measure the distance from the origin to point A' in triangle A'B'C':
\[
d_{A'B'C'} = \sqrt{(kx_1)^2 + (ky_1)^2} = k \cdot d_{ABC}
\]

The dilation factor \(k\) is the same for all points, meaning:
\[
k = \frac{d_{A'B'C'}}{d_{ABC}}
\]

You will need the actual coordinates or distances to calculate this ratio numerically. If you provide the coordinates or distance measurements related to triangle ABC and triangle A'B'C', I can certainly help you find the specific magnitude of the dilation.