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Method and examples
Method  
Distance between two points

1. Distance, Slope of two points
 
1. Find the distance between the points A(5,-8) and B(-7,-3)
2. Find the slope of the line joining points A(4,-8) and B(5,-2)

A ( , ) , B ( , )
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Find the value of x or y
 
3. If distance between the points (5,3) and (x,-1) is 5, then find the value of x.
A ( , ) , B ( , ) , Distance =
 
 
4. If slope of the line joining points A(x,0), B(-3,-2) is 2/7, find the value of x
A ( , ) , B ( , ) , Slope =
 

Mode =
Decimal Place =
SolutionMethods
Distance between two points calculator
1. Find the distance between the points A(5,-8) and B(-7,-3)
2. Find the distance between the points A(7,-4) and B(-5,1)
3. Find the distance between the points A(-6,-4) and B(9,-12)
4. Find the distance between the points A(1,-3) and B(4,-6)
5. Find the distance between the points A(-5,7) and B(-1,3)
6. Find the distance between the points A(-8,6) and B(2,0)
7. Find the distance between the points A(0,0) and B(7,4)


Example
1. Find the distance between the points A(5,-8) and B(-7,-3)

Solution:
Points are A(5,-8),B(-7,-3)

:. x_1=5,y_1=-8,x_2=-7,y_2=-3

AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

AB=sqrt((-7-5)^2+(-3+8)^2)

=sqrt((-12)^2+(5)^2)

=sqrt(144+25)

=sqrt(169)

:. AB=13




2. Find the distance between the points A(7,-4) and B(-5,1)

Solution:
Points are A(7,-4),B(-5,1)

:. x_1=7,y_1=-4,x_2=-5,y_2=1

AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

AB=sqrt((-5-7)^2+(1+4)^2)

=sqrt((-12)^2+(5)^2)

=sqrt(144+25)

=sqrt(169)

:. AB=13




3. Find the distance between the points A(-6,-4) and B(9,-12)

Solution:
Points are A(-6,-4),B(9,-12)

:. x_1=-6,y_1=-4,x_2=9,y_2=-12

AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

AB=sqrt((9+6)^2+(-12+4)^2)

=sqrt((15)^2+(-8)^2)

=sqrt(225+64)

=sqrt(289)

:. AB=17




4. Find the distance between the points A(1,-3) and B(4,-6)

Solution:
Points are A(1,-3),B(4,-6)

:. x_1=1,y_1=-3,x_2=4,y_2=-6

AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

AB=sqrt((4-1)^2+(-6+3)^2)

=sqrt((3)^2+(-3)^2)

=sqrt(9+9)

=sqrt(18)

:. AB=3sqrt(2)




5. Find the distance between the points A(-5,7) and B(-1,3)

Solution:
Points are A(-5,7),B(-1,3)

:. x_1=-5,y_1=7,x_2=-1,y_2=3

AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

AB=sqrt((-1+5)^2+(3-7)^2)

=sqrt((4)^2+(-4)^2)

=sqrt(16+16)

=sqrt(32)

:. AB=4sqrt(2)




6. Find the distance between the points A(-8,6) and B(2,0)

Solution:
Points are A(-8,6),B(2,0)

:. x_1=-8,y_1=6,x_2=2,y_2=0

AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

AB=sqrt((2+8)^2+(0-6)^2)

=sqrt((10)^2+(-6)^2)

=sqrt(100+36)

=sqrt(136)

:. AB=2sqrt(34)




7. Find the distance between the points A(0,0) and B(7,4)

Solution:
Points are A(0,0),B(7,4)

:. x_1=0,y_1=0,x_2=7,y_2=4

AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

AB=sqrt((7-0)^2+(4-0)^2)

=sqrt((7)^2+(4)^2)

=sqrt(49+16)

=sqrt(65)

:. AB=sqrt(65)







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