Triangle ABC is dilated about the origin to create triangle A′B′C′.

Question

Triangle ABC with vertices at A negative 13 comma negative 4, B negative 6 comma negative 4, and C negative 6 comma 4 and triangle A prime B prime C prime with vertices at A prime negative 32.5 comma negative 10, B prime negative 15 comma negative 10, and C prime negative 15 comma 10.

Determine the scale factor used to create the image.

three fourths
2
one half
2.5

Answer 1

The scale factor used to create the image is 2.

This can be determined by looking at how the x and y coordinates of each vertex have changed. For example, the x-coordinate of point A has changed from -13 to -32.5, which is a change of 19.5. Similarly, the y-coordinate of point A has changed from -4 to -10, which is a change of 6.

Since both changes are multiplied by the same number, the scale factor is 2.