3)The circumference and area of the circle are
4√2π units and 8π unit²
4) The circumference and area of the circle are
2√5π units and 5π unit².
How the area and circumference of the circles were calculated.
Distance between two points (x₁, y₁) and (x₂₂, y₂),can be found by the distance formula:
Distance = √(x₂ - x₁)² + (y₂ - y₁)²
For points (2,3) and (4,1)
Distance = √(4-2)² + (1-3)²
= √2² + (-2)²
= √4 + 4
= √8
= 2√2
Radius of the circle = 2√2
Circumference = 2πr
= 2*π*2√2
= 4√2π units
Area = πr²
= π(2√2)²
= 8π unit²
4) For the points (-3, 4) and (-4, 2)
Distance = √(-4 - (-3))² + (2 - 4)²
= √((-1)² + (-2)²
= √1 + 4
= √5
Circumference = 2πr
= 2*π*√5
= 2√5π units
Area = πr²
= π(√5)²
= 5π unit²