The points (-18, 15) and (-20, 15) lie on a circle with a radius of 1. Find the coordinates of the center of the circle.​

Step-by-step explanation:

eq. of any circle with center (h,k) and r=1 is

(x-h)²+(y-k)²=1²

points (-18,15) and (-20,15) lie on it.

(-18-h)²+(15-k)²=1

(15-k)²=1-(-18-h)²

and (-20-h)²+(15-k)²=1

(15-k)²=1-(-20-h)²

so 1-(-18-h)²=1-(-20-h)²

-(18+h)²=-(20+h)²

324+36h+h²=400+40h+h²

40h-36h=324-400

4h=-76

h=-19

(15-k)²=1-(-18-(-19))²=1-1=0

k=15

so center is (-19,15)

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step-by-step explanation:

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2