Question

Show that the points (3, 4) (-3, 4) (4, -3) lie on a circle with center at the origin

Answer 1

Answer:

The given points lie on a circle with centre at the origin.

Step-by-step explanation:

The distance between the origin and any point on a circle is same.

Hence, we need to prove that the distance between the given points and the origin is same.

Let the origin be O ≡ (0,0)

Let the points be A ≡ (3,4) ; B ≡ (-3,4) ; C ≡ (4,-3)

Distance between the origin (0,0) and a point (x,y) = √{(x-0)²+(y-0)²}

Therefore,

Distance between OA = √{(3-0)²+(4-0)²} = √{(3)²+(4)²} =√{9+16} = √{25} = 5

Distance between OB = √{(-3-0)²+(4-0)²} = √{(-3)²+(4)²} =√{9+16} = √{25} = 5

Distance between OC = √{(4-0)²+(-3-0)²} = √{(4)²+(-3)²} =√{16+9} = √{25} = 5

Since, OA = OB = OC,

The points are equidistant from the origin.

Hence, the given points lie on a circle with the centre at the origin.