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`

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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`

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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`

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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)`

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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)`

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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)`

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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)`