Find the distance between the following pairs of points : (i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b)

(i) A(2,3), B(4,1)
Using the distance formula: √((x₂-x₁)²+(y₂-y₁)²)
Distance between A(2,3) and B(4,1) is given by AB
= √((4-2)²+(1-3)²) = √(4+4) = √8 = 2√2

(ii) P(-5,7), Q(-1,3)
Using the distance formula: √((x₂-x₁)²+(y₂-y₁)²)
Distance between P(-5,7) and Q(-1,3) is given by PQ
= √((-1-(-5))²+(3-7)²) = √(16+16) = √32 = 4√2

(iii) M(a,b), N(-a,-b)
Using the distance formula: √((x₂-x₁)²+(y₂-y₁)²)
Distance between M(a,b) and N(-a,-b) is given by MN
= √(-a-(a))²+(-b-(-b))²) = √(4a²+4b²) = 2√(a²+b²)

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