Question

30 points I really need your help pronto!

Answer 1

Answer:

Part 1) the center is $(2,-1)$, the radius is $4\ units$

Part 2) see the procedure

Part 3) $m$

Step-by-step explanation:

Part 1) we know that

The equation of a circle in center radius form is equal to

$(x-h)^{2}+(y-k)^{2} =r^{2}$

where

(h,k) is the center of the circle

r is the radius

In this problem we have

$(x-2)^{2}+(y+1)^{2} =16$

so

the center is the point $(2,-1)$

the radius is $r=\sqrt{16}=4\ units$

Part 2) we know that

The center of circle F' is$(-2,-8)$ and the radius is  $r=2\ units$

The center of circle F is$(6,-6)$ and the radius is  $r=4\ units$

step 1

Move the center of the circle F' onto the center of the circle F

the transformation has the following rule

$(x,y)--------> (x+8,y+2)$

8 units right and 2 units up

so

$(-2,-8)--------> (-2+8,-8+2)-----> (6,-6)$

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

$(x+16)+(x)+(6x-4)+(2x+16)=360\°$

solve for x

$(10x+28)=360\°$

$10x=360\°-28\°$

$x=332\°/10=33.2\°$

The measure of angle B is

$m$

so

$m$