We know that:
![(x-a)^2+(y-b)^2=r^2](https://tex.z-dn.net/?f=%28x-a%29%5E2%2B%28y-b%29%5E2%3Dr%5E2)
is an equation of a circle.
When we substitute x and y (from the pairs we have), we'll get a system of equations:
![\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%28-1-a%29%5E2%2B%282-b%29%5E2%3Dr%5E2%5C%5C%280-a%29%5E2%2B%281-b%29%5E2%3Dr%5E2%5C%5C%28-2-a%29%5E2%2B%28-1-b%29%5E2%3Dr%5E2%5Cend%7Bcases%7D)
and all we have to do is solve it for a, b and r.
There will be:
![\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}\\\\\\ \begin{cases}1+2a+a^2+4-4b+b^2=r^2\\a^2+1-2b+b^2=r^2\\4+4a+a^2+1+2b+b^2=r^2\end{cases}\\\\\\ \begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\\\\\ ](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%28-1-a%29%5E2%2B%282-b%29%5E2%3Dr%5E2%5C%5C%280-a%29%5E2%2B%281-b%29%5E2%3Dr%5E2%5C%5C%28-2-a%29%5E2%2B%28-1-b%29%5E2%3Dr%5E2%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D1%2B2a%2Ba%5E2%2B4-4b%2Bb%5E2%3Dr%5E2%5C%5Ca%5E2%2B1-2b%2Bb%5E2%3Dr%5E2%5C%5C4%2B4a%2Ba%5E2%2B1%2B2b%2Bb%5E2%3Dr%5E2%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7Da%5E2%2Bb%5E2%2B2a-4b%2B5%3Dr%5E2%5C%5Ca%5E2%2Bb%5E2-2b%2B1%3Dr%5E2%5C%5Ca%5E2%2Bb%5E2%2B4a%2B2b%2B5%3Dr%5E2%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%0A)
From equations (II) and (III) we have:
![\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Da%5E2%2Bb%5E2-2b%2B1%3Dr%5E2%5C%5Ca%5E2%2Bb%5E2%2B4a%2B2b%2B5%3Dr%5E2%5Cend%7Bcases%7D%5C%5C--------------%28-%29%5C%5C%5C%5Ca%5E2%2Bb%5E2-2b%2B1-a%5E2-b%5E2-4a-2b-5%3Dr%5E2-r%5E2%5C%5C%5C%5C-4a-4b-4%3D0%5Cqquad%7C%3A%28-4%29%5C%5C%5C%5C%5Cboxed%7B-a-b-1%3D0%7D%20)
and from (I) and (II):
![\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Da%5E2%2Bb%5E2%2B2a-4b%2B5%3Dr%5E2%5C%5Ca%5E2%2Bb%5E2-2b%2B1%3Dr%5E2%5Cend%7Bcases%7D%5C%5C--------------%28-%29%5C%5C%5C%5Ca%5E2%2Bb%5E2%2B2a-4b%2B5-a%5E2-b%5E2%2B2b-1%3Dr%5E2-r%5E2%5C%5C%5C%5C2a-2b%2B4%3D0%5Cqquad%7C%3A2%5C%5C%5C%5C%5Cboxed%7Ba-b%2B2%3D0%7D)
Now we can easly calculate a and b:
![\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D-a-b-1%3D0%5C%5Ca-b%2B2%3D0%5Cend%7Bcases%7D%5C%5C--------%28%2B%29%5C%5C%5C%5C-a-b-1%2Ba-b%2B2%3D0%2B0%5C%5C%5C%5C-2b%2B1%3D0%5C%5C%5C%5C-2b%3D-1%5Cqquad%7C%3A%28-2%29%5C%5C%5C%5C%5Cboxed%7Bb%3D%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C%5C%5Ca-b%2B2%3D0%5C%5C%5C%5C%5C%5Ca-%5Cdfrac%7B1%7D%7B2%7D%2B2%3D0%5C%5C%5C%5C%5C%5Ca%2B%5Cdfrac%7B3%7D%7B2%7D%3D0%5C%5C%5C%5C%5C%5C%5Cboxed%7Ba%3D-%5Cfrac%7B3%7D%7B2%7D%7D)
Finally we calculate
![r^2](https://tex.z-dn.net/?f=r%5E2)
:
![a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2-2b%2B1%3Dr%5E2%5C%5C%5C%5C%5C%5C%5Cleft%28-%5Cdfrac%7B3%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%5E2-2%5Ccdot%5Cdfrac%7B1%7D%7B2%7D%2B1%3Dr%5E2%5C%5C%5C%5C%5C%5C%5Cdfrac%7B9%7D%7B4%7D%2B%5Cdfrac%7B1%7D%7B4%7D-1%2B1%3Dr%5E2%5C%5C%5C%5C%5C%5C%5Cdfrac%7B10%7D%7B4%7D%3Dr%5E2%5C%5C%5C%5C%5C%5C%5Cboxed%7Br%5E2%3D%5Cfrac%7B5%7D%7B2%7D%7D)
And the equation of the circle is:
Answer:
68.8
Step-by-step explanation:
(a+b)h/2
12.9+8.6 *6.4/2
A' = (-6, 2), B' = (-3/2, 4), C' = (9/2, 3), D' = (3, -2) and E' = (-3, -1). The new figure is similar to the original figure
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
A horizontal stretch by a factor of k uses the rule: (x,y) → (kx, y). Pentagon ABCDE is stretched horizontally by a factor of 3/2, hence:
A' = (-6, 2), B' = (-3/2, 4), C' = (9/2, 3), D' = (3, -2) and E' = (-3, -1)
The new figure is similar to the original figure
Find out more on equation at: brainly.com/question/2972832
#SPJ1
270, 360 | 2
135, 180 | 3
45, 60 | 3
15, 20 | 5
3, 4
2 * 3 * 3 * 5 = 90
The greatest common factor of 270 and 360 is 90.