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 determine the magnitude of dilation for triangle ABC to triangle A'B'C', we need to compare the coordinates of the vertices of both triangles relative to the origin.

The formula for the magnitude of dilation is given by:

\[
k = \frac{\text{Distance from the origin to a vertex of } A'B'C'}{\text{Distance from the origin to the corresponding vertex of } ABC}
\]

If the coordinates of vertex A in triangle ABC are (x, y) and its corresponding vertex A' in triangle A'B'C' is (kx, ky) after dilation, then:

\[
k = \frac{\sqrt{(kx)^2 + (ky)^2}}{\sqrt{x^2 + y^2}} = \frac{k \sqrt{x^2 + y^2}}{\sqrt{x^2 + y^2}} = k
\]

Therefore, to find the magnitude of dilation \( k \), you simply look at the ratio of distances from the origin to each corresponding vertex.

Since I can't see the image you're referring to, make sure to plug in the coordinates or corresponding distances to find the value of \( k \).

If you provide the coordinates or distance measurements, I can help you further in calculating the magnitude of dilation.