Distance Formula
Key Questions

Answer:
Let's see.
Explanation:
I have drawn a graph in which there are two points
#color(red)(p_1(x_1,y_1))" and "color(red)(p_2(x_2,y_2)# . We can easily say that
#" "bar(OD)=x_1" ; "bar(OE)=x_2" ; "bar(AD)=y_1" ; "bar(EB)=y_2#
We also have a rectangle
#square OCED# . So,#color(red)(bar(AC)=bar(DE)) " and "color(red)(bar(AD)=bar(CE)# Now,

#bar(AC)=bar(DE)=bar(OE)bar(OD)=(x_2 x_1)# 
#bar(BC)=bar(BE)bar(CE)=bar(BE)bar(AD)=(y_2y_1)#
With the help of Pythagorean theorem,
#bar(AB)^2=bar(BC)^2+bar(AC)^2# #bar(AB)^2=(x_2x_1)^2+(y_2y_1)^2# #bar(AB)=sqrt((x_2x_1)^2+(y_2y_1)^2# N.B: As it is a square value , you may take
#(x_1x_2)# or,#(x_2x_1)# . I mean you have to take difference.That's#(x_1~x_2)# So, the required formula is proved that
If the distance between two points
#color(green)(p_1(x_1,y_1)# and#color(green)(p_2(x_2,y_2)# is#color(red)(r# ,then,
#color(red)(ul(bar(color(green)(r=sqrt((x_1x_2)^2+(y_1y_2)^2))# Hope it helps...
Thank you...  We can easily say that

Distance Formula
The distance
#D# between two points#(x_1,y_1)# and#(x_2,y_2)# can be found by#D=sqrt{(x_2x_1)^2+(y_2y_1)^2}#
Example
Find the distance between the points
#(1,2)# and#(5,1)# .Let
#(x_1,y_1)=(1,2)# and#(x_2,y_2)=(5,1)# .By Distance Formula above,
#D=sqrt{(51)^2+[1(2)]^2}=sqrt{16+9}=sqrt{25}=5#
I hope that this was helpful.

Given the two points
#(x_1, y_1)# and#(x_2, y_2)# the distance between these points is given by the formula:#d=sqrt((x_2x_1)^2+(y_2y_1)^2 )# All you have to do is plug in the given points given to the distance formula and solve.
Questions
Radicals and Geometry Connections

Graphs of Square Root Functions

Simplification of Radical Expressions

Addition and Subtraction of Radicals

Multiplication and Division of Radicals

Radical Equations

Pythagorean Theorem and its Converse

Distance Formula

Midpoint Formula

Measures of Central Tendency and Dispersion

StemandLeaf Plots

BoxandWhisker Plots