Answer:
Part 1) the center is , the radius is
Part 2) see the procedure
Part 3)
Step-by-step explanation:
Part 1) we know that
The equation of a circle in center radius form is equal to
where
(h,k) is the center of the circle
r is the radius
In this problem we have
so
the center is the point
the radius is
Part 2) we know that
The center of circle F' is and the radius is
The center of circle F is and the radius is
step 1
Move the center of the circle F' onto the center of the circle F
the transformation has the following rule
8 units right and 2 units up
so
center circle F' is now equal to center circle F
The circles are now concentric (they have the same center)
step 2
A dilation is needed to increase the size of circle F' to coincide with circle F
scale factor=radius circle F/radius circle F'=4/2=2
radius circle F' will be=2*scale factor=2*2=4 units
radius circle F' is now equal to radius circle F
A translation, followed by a dilation will map one circle onto the other
Part 3) we know that
The sum of the interior angles in a quadrilateral is equal to 360 degrees
so
substitute the values
solve for x
The measure of angle B is
so