Show that Circle R with center (2, -9) and radius 5 is similar to Circle Q with center (-4, 3) and radius 3 by using a series of transformations that maps Circle R to Circle Q.

It can be proved that the circle R is similar to the circle Q by translating the circle R a displacement of (-6, 12).

Step-by-step explanation:

We can demonstrate that Circle R is similar to Circle Q by translating the center of the former one to the center of latter one. Meaning that every point of circle R experiments the same translation. Vectorially speaking, a translation is defined by:

(1)

Where:

- Original point.

- Translated point.

- Translation vector.

If we know that and , then the translation vector is:

It can be proved that the circle R is similar to the circle Q by translating the circle R a displacement of (-6, 12).

A.  The y-intercept is y = −0.05 x + 16 and the x-intercept is x = −20y + 320

B. The x-intercept represents the number of miles the car has traveled.

C. The y-intercept represents the number of gas in gallons.