Question:

Find the distance between each of the following pairs of points.

(1)A(2, 3), B(4, 1)
(2) P(-5, 7), Q(-1, 3)
(3) R(0, -3), S(0, 5/2 )

Answer:

(1) Let A(x1, y1) and B(x2 , y2) be the given points
By distance formula d(A,B) = √[(x2-x1)2+(y2-y1)2]
Here x1 = 2, y1 = 3 , x2 = 4, y2 = 1
d(A,B) = √[(4-2)2+(1-3)2]
= √[22+(-2)2]
= √8
= 2√2
Hence the distance between A and B is 2√2 units.


(2) Let P(x1, y1) and Q(x2 , y2) be the given points
By distance formula d(P,Q) = √[(x2-x1)2+(y2-y1)2]
Here x1 = -5, y1 = 7 , x2 = -1, y2 = 3
d(A,B) = √[(-1-(-5))2+(3-7)2]
= √[42+(-4)2]
= √32
= 4√2
Hence the distance between P and Q is 4√2 units.

(3) Let R(x1, y1) and S(x2 , y2) be the given points
By distance formula d(R,S) = √[(x2-x1)2+(y2-y1)2]
Here x1 = 0, y1 = -3 , x2 = 0, y2 = 5/2
d(A,B) = √[(0-0)2+((5/2) -(-3))2]
= √[02+(11/2)2]
= √(121/4)
= 11/2
Hence the distance between P and Q is 11/2 units.

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