Question

Find the distance between the following pairs of points.
I) (2,3)(4,1)
ii) (-5,7)(-1,3)
iii) (a,b),(−a,−b)


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Answer 1

Question

find the distance between the following pair of point ;

• (2,3)(4,1)
• (-5,7)(-1,3)
• (a,b)(-a,-b)

Solution

we can solve this by using the formula of distance .

• √ (x2-x1)^2+(y2-y1)^2

i) (2,3)(4,1)

x1=-2

y1=3

x2 = 4

y2=1

putting the values in the formula ;

Now,

PQ = √(4-2)^2+(1-3)^2

=> √(2)^2+(2)^2

=> √4+4

=> √8

=> 4√2

=> 2√2 unit

ii) (-5,7)(-1,3)

let's take

x1 = -5

y1 = 7

x2=-1

y2=3

now putting the value in the formula;

=> √{(-1)-(5)}^2 + (3-7)^2

=> √(-1+5)^2+(-4)^2

=> √(4)^2+(-4)^2

=>√16+16

=>√32

=>4√2 unit

iii) (a,b)(-a,-b)

let's take

x1=a

y1=b

x2=-a

y2=-b

now putting the value in the formula;

=>√(-a-(a))^2+(b-(b))^2

=>√(a+a)^2+(b+b)^2

=>√2a^2+2b^2

=>√4a^2+4b^2

=>√4+a^2+b^2

=>√4×a^2+b^2