Points (–9, 2) and (–5, 6) are endpoints of the diameter of a circle

Question

(a) What is the length of the diameter? Give the exact answer?

Answer 1

The end points of the diameter of a circle are (- 9, 2) and (- 5, 6).

Length of the diameter is distance between the end points of the diameter of the circle.

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

Substitute the values of a(X₁, y₁) = (- 9, 2) and b(X₂, y₂) = (- 5, 6) in the distance formula : √[ (X₂ - X₁)² + (y₂ - y₁)² ].

Length of the diameter = √[ (- 5 - (- 9))² + (6 - 2)² ]

                                     = √[ (- 5 + 9)² + (4)² ]

                                     = √[ (4)² + (4)² ]

                                     = √[16+ 16]

                                     = √32

                                     = 4√2.

Therefore, length of the diameter is 4√2 units.