Review of Coordinate Geometry: the Distance Formula, the Midpoint Formula

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 $\,(x_1,y_1)\,$ and $\,(x_2,y_2)\,$ is given by the Distance Formula: $$ \cssId{s10}{\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}} $$

For a complete review of the distance between two points in the coordinate plane, study the following lesson,
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: $$ \cssId{s25}{\left( \frac{x_1+x_2}2,\frac{y_1+y_2}2 \right)} $$

For a complete review of midpoints, including a derivation and examples, study: The Midpoint Formula

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Sketching Regions in the Coordinate Plane

DISTANCE BETWEEN POINTS; THE MIDPOINT FORMULA

The Distance Formula

The Midpoint Formula