The Distance Formula
To find the distance between any two points in a coordinate plane:
- subtract the $x$-values in any order; square the result
- subtract the $y$-values in any order; square the result
- add together the previous two quantities
- take the square root of the result
This sequence of operations is expressed in the Distance Formula:
the Distance Formula
The distance between points
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$\,(x_1,y_1)\,$
and
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$\,(x_2,y_2)\,$
is given by the Distance Formula:
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$$
\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
$$
For a complete review of the distance between two points in the coordinate plane, study the following web exercise,
which includes a derivation, a discussion of subscript notation, and examples: The Distance Formula
The Midpoint Formula
To find the midpoint of the line segment between any two points in a coordinate plane:
- average the $x$-values of the two points—that is, add them and divide by $2$;
this gives the $x$-value of the midpoint
- average the $y$-values of the two points—that is, add them and divide by $2$;
this gives the $y$-value of the midpoint
This sequence of operations is expressed in the Midpoint Formula:
THE MIDPOINT FORMULA
The midpoint of the line segment between points
$\,(x_1,y_1)\,$
and
$\,(x_2,y_2)\,$
is given by the Midpoint Formula:
$$
\left(
\frac{x_1+x_2}2,\frac{y_1+y_2}2
\right)
$$
For a complete review of midpoints, including a derivation and examples, study:
The Midpoint Formula