Step-by-step explanation:
(1) Find the distance between the two points (3,4) and (4,7).
Explanation:-
Distance formulae:
Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}
Let's figure out the distance between two points A = (3,4) and B = (4,7).
From those points,
x₁ = 3
x₂ = 4
y₁ = 4
y₂ = 7
Using them in the formula,
Distance btw AB = [(4-3}² + (7-4)²]
= √[(1)² + (3)²]
= √[(1*1)² + (5*5)²]
= √[1 + 25]
= √[26] = 13 Units.
Therefore, the distance between A(3,4) and B(4,7) is 13 units.
Similarly,
(2). (8, 4) and (6, 10)
Distance = √{(x₂ - x₁)² + (y₂ - y₁)²} ←Formula
From those points,
x₁ = 8
x₂ = 6
y₁ = 4
y₂ = 10
Using them in the formula,
Distance btw AB = √[(6-8)²+(10-4)²]
= √[(-2)²+(-6)²]
= √[(-2*-2) + (-6*-6)]
= √[4+36]
= √[40] = 6.324 Units.
Therefore, the distance between A(8,4) and B(6,10) is 6.324 units.
(2). (3, -1) and (7,-5)
Distance = √{(x₂ - x₁)² + (y₂ - y₁)²} ←Formula
From those points,
x₁ = 3
x₂ = 7
y₁ = -1
y₂ = -5
Using them in the formula,
Distance btw AB = √[(7-3)²+{-5-(-1)}²]
= √[(4)²+(-5+1)²]
= √[(4)² + (-4)²]
= √[(4*4)+(-4*-4)
= √[16+16]
= √[32] = 4√2 Units.
Therefore, the distance between A(3,-1) and B(7,-5) is 4√2 units.
