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DᴀʀᴋPᴀʀᴀᴅᴏx

[tex] \qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

Here's the solution ~

Figure 1 :

Centre (A) = (0 , 0)

let's use distance formula to find the Radius (AB) :

[tex]\qquad \sf \dashrightarrow \: \sqrt{(2- 0) {}^{2} + (0- 0) {}^{2} } [/tex]

[tex]\qquad \sf \dashrightarrow \: \sqrt{(2) {}^{2} + 0} [/tex]

[tex]\qquad \sf \dashrightarrow \: \sqrt{2 {}^{2} } [/tex]

[tex]\qquad \sf \dashrightarrow \: 2[/tex]

Radius = 2 units

Figure 2 :

Centre (A)= (2 , 1)

Let's solve for radius (AB) :

[tex]\qquad \sf \dashrightarrow \: \sqrt{(2 - 2) { }^{2} + (3 - 1) {}^{2} } [/tex]

[tex]\qquad \sf \dashrightarrow \: \sqrt{0 + (2) {}^{2} } [/tex]

[tex]\qquad \sf \dashrightarrow \: \sqrt{2 {}^{2} } [/tex]

[tex]\qquad \sf \dashrightarrow \: 2[/tex]

Radius = 2 units

Figure 3 :

Centre = (0 , -2)

now, let's find the Radius (AB) :

[tex]\qquad \sf \dashrightarrow \: \sqrt{ ( - 3 - 0) {}^{2} + ( - 2 - ( - 2)) {}^{2} }[/tex]

[tex]\qquad \sf \dashrightarrow \: \sqrt{( - 3) {}^{2} + 0} [/tex]

[tex]\qquad \sf \dashrightarrow \: \sqrt{( - 3) {}^{2} } [/tex]

[tex]\qquad \sf \dashrightarrow \: \sqrt{9} [/tex]

[tex]\qquad \sf \dashrightarrow \: 3[/tex]

Radius = 3 units

mhanifa

Answer:

  • See below

Step-by-step explanation:

Determine the center by coordinates (x, y) of point A.

Determine the radius by the difference of respective coordinates of the A and B points (the center and the point on the circle).

#1

Points given:

  • A = (0, 0) and B = (2, 0)
  • The center is (0, 0)
  • The radius  is 2 - 0 = 2 units (the distance between two horizontal points)

#2

Points given:

  • A = (2, 1) and B = (2, 3)
  • The center is (2, 1)
  • The radius  is 3 - 1 = 2 units (the distance between two vertical points)

#3

Points given:

  • A = (0, -2) and B = (-3, -2)
  • The center is (0, -2)
  • The radius  is 0 - (-3) = 3 units  (the distance between two horizontal points)

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