Distance between two points calculator

SolutionMethods

1. Find the distance between the points

A(5,-8) $A(5,-8)$ and

B(-7,-3) $B(-7,-3)$

2. Find the distance between the points

A(7,-4) $A(7,-4)$ and

B(-5,1) $B(-5,1)$

3. Find the distance between the points

A(-6,-4) $A(-6,-4)$ and

B(9,-12) $B(9,-12)$

4. Find the distance between the points

A(1,-3) $A(1,-3)$ and

B(4,-6) $B(4,-6)$

5. Find the distance between the points

A(-5,7) $A(-5,7)$ and

B(-1,3) $B(-1,3)$

6. Find the distance between the points

A(-8,6) $A(-8,6)$ and

B(2,0) $B(2,0)$

7. Find the distance between the points

A(0,0) $A(0,0)$ and

B(7,4) $B(7,4)$

Example

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

Solution:
Points are

A(5,-8),B(-7,-3) $A(5,-8),B(-7,-3)$

∴x1=5,y1=-8,x2=-7,y2=-3 $:. x_1=5,y_1=-8,x_2=-7,y_2=-3$

AB=√(x2-x1)2+(y2-y1)2 $AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

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

=√(-12)2+(5)2 $=sqrt((-12)^2+(5)^2)$

=√144+25 $=sqrt(144+25)$

=√169 $=sqrt(169)$

∴AB=13 $:. AB=13$

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

Solution:
Points are

A(7,-4),B(-5,1) $A(7,-4),B(-5,1)$

∴x1=7,y1=-4,x2=-5,y2=1 $:. x_1=7,y_1=-4,x_2=-5,y_2=1$

AB=√(x2-x1)2+(y2-y1)2 $AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

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

=√(-12)2+(5)2 $=sqrt((-12)^2+(5)^2)$

=√144+25 $=sqrt(144+25)$

=√169 $=sqrt(169)$

∴AB=13 $:. AB=13$

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

Solution:
Points are

A(-6,-4),B(9,-12) $A(-6,-4),B(9,-12)$

∴x1=-6,y1=-4,x2=9,y2=-12 $:. x_1=-6,y_1=-4,x_2=9,y_2=-12$

AB=√(x2-x1)2+(y2-y1)2 $AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

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

=√(15)2+(-8)2 $=sqrt((15)^2+(-8)^2)$

=√225+64 $=sqrt(225+64)$

=√289 $=sqrt(289)$

∴AB=17 $:. AB=17$

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

Solution:
Points are

A(1,-3),B(4,-6) $A(1,-3),B(4,-6)$

∴x1=1,y1=-3,x2=4,y2=-6 $:. x_1=1,y_1=-3,x_2=4,y_2=-6$

AB=√(x2-x1)2+(y2-y1)2 $AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

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

=√(3)2+(-3)2 $=sqrt((3)^2+(-3)^2)$

=√9+9 $=sqrt(9+9)$

=√18 $=sqrt(18)$

∴AB=3√2 $:. AB=3sqrt(2)$

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

Solution:
Points are

A(-5,7),B(-1,3) $A(-5,7),B(-1,3)$

∴x1=-5,y1=7,x2=-1,y2=3 $:. x_1=-5,y_1=7,x_2=-1,y_2=3$

AB=√(x2-x1)2+(y2-y1)2 $AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

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

=√(4)2+(-4)2 $=sqrt((4)^2+(-4)^2)$

=√16+16 $=sqrt(16+16)$

=√32 $=sqrt(32)$

∴AB=4√2 $:. AB=4sqrt(2)$

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

Solution:
Points are

A(-8,6),B(2,0) $A(-8,6),B(2,0)$

∴x1=-8,y1=6,x2=2,y2=0 $:. x_1=-8,y_1=6,x_2=2,y_2=0$

AB=√(x2-x1)2+(y2-y1)2 $AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

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

=√(10)2+(-6)2 $=sqrt((10)^2+(-6)^2)$

=√100+36 $=sqrt(100+36)$

=√136 $=sqrt(136)$

∴AB=2√34 $:. AB=2sqrt(34)$

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

Solution:
Points are

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

∴x1=0,y1=0,x2=7,y2=4 $:. x_1=0,y_1=0,x_2=7,y_2=4$

AB=√(x2-x1)2+(y2-y1)2 $AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

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

=√(7)2+(4)2 $=sqrt((7)^2+(4)^2)$

=√49+16 $=sqrt(49+16)$

=√65 $=sqrt(65)$

∴AB=√65 $:. AB=sqrt(65)$