If a (2 -1) and b (4 7) are the endpoints of a diameter of a circle what is the area on the circle?

Question

A) 16pi 
B) 17 pi 
C) 18 pi 
D) 144 pi 
E) 1156 pi

Answer 1

Area of the circle ( A ) = πr²

^{The end points of the diameter are a(2, - 1) and b(4, 7).}

Diameter(d) = 2r = distance between the end points of the diameter.

distance formula : √[ (X₂ - X₁)² + (y₂ - y₁)² ].

Substitute the values of a(X₁, y₁) = (2, - 1) and b(X₂, y₂) = (4, 7) in the distance formula : √[ (X₂ - X₁)² + (y₂ - y₁)² ].

d = 2r = √[ (4 - 2)² + (7 + 1)² ]

2r = √[ (2)² + (8)² ] = √[ 4 + 64 ] =  √68.

⇒ r = √68/2.

Substitute the value of r = √68/2 in area of the circle : A = πr².

A = π(√68/2)² = (68/4)π = 17π.

Therefore, area of the circle is 17π square units.

The right choice is B.