1. Find the distance between the points A(5,-8) and B(-7,-3)
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)`
This material is intended as a summary. Use your textbook for detail explanation.
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