Question

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.

Answer 1

Answer:

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:

$O'(x,y) = O(x,y) + T(x,y)$ (1)

Where:

$O(x,y)$ - Original point.

$O'(x,y)$ - Translated point.

$T(x,y)$ - Translation vector.

If we know that $O(x,y) = (2,-9)$ and $O'(x,y) = (-4,3)$, then the translation vector is:

$T(x,y) = O'(x,y)-O(x,y)$

$T(x,y) = (-4,3) - (2,-9)$

$T(x,y) = (-6,12)$

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