FINDING DISTANCE BETWEEN TWO POINTS PRACTICE

Find the distance between the following points.

(i)  A (3, 7) and B (6, 5)

(ii)  P (1,1) and Q (5,4)

(iii)  R (5,4) and S (-2,5)

(iv)  S (4,6) and T (7,7)

(v)  N (2,6) and R (5,1)

Detailed Solutions

Distance between two points 

  =  √(x₂ - x₁)² + (y₂ - y₁)²

(i)

Here x₁  =  3, y₁  =  7,  x₂  =  6  and  y₂  =  5

Distance between A and B  =  √(6-3)² + (5-7)²

  =  √(3)² + (-2)²

  =  √(9+4)

  =  √13 units

(ii)  

Here x₁  =  1, y₁  =  1,  x₂  =  5  and  y₂  =  4

Distance between P and Q  =  √(5 - 1)² + (4 - 1)²

  =  √4² + 3²

  =  √16+9

  =  √25

  =  5 units

(iii) 

Here x₁  =  5, y₁  =  4,  x₂  =  -2  and  y₂  =  5

Distance between S and R  =  √(-2-5)² + (5-4)²

=  √(-7)² + 1²

=  √(49+1)

=  √50

=  √(5 ⋅ 5 ⋅ 2)

=  5√2 units

(iv) 

Here x₁  =  4, y₁  =  6,  x₂  =  7  and  y₂  =  7

Distance between S and T  =  √(7-4)² + (7-6)²

=  √3²+1²

=  √(9+1)

=  √10 units

(v)

Here x₁  =  2, y₁  =  6,  x₂  =  5  and  y₂  =  1

Distance between N and R  =  √(5-2)² + (1-6)²

=  √3²+(-5)²

=  √(9+25)

=  √34 units

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