Distance between two points calculator

SolutionMethods

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

$A(0,0),B(7,4)$

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

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

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

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

$=sqrt(49+16)$

$=sqrt(65)$

$:. AB=sqrt(65)$