Ordered pairs of numbers form a two-dimensional region x-axis: horizontal line y-axis: vertical line Axes intersect at origin O (0,0) and divide plane into 4 parts

2.1 Coordinate Plane

x

y

Distance Formula

x

y A

B

Point A has coordinates:Point B has coordinates:

Vertical distance, v, is

Horizontal distance, h, is

),( 11 yx),( 22 yx

dv

h

Distance Formula(continued)

x

y A

B

d

Since we are dealing with a right triangle:

v

h

And:

So, given any two points, you can find the distance between them.

Example 1Find the distance between (5, 4) and (2, -1).

First, draw both points and make a guess.

Example 2Find the point on the y-axis that is equidistant from the points (1, 2) and (4, -2).

First, draw both points and make a guess.

Whatever the point, need the distance from it to point 1 to be the same as the distance from it to point 2. Also, we know that any point on the y-axis has

Example 2(continued)(1,2)

(4,-2)

Need both distances to equal.

Midpoint FormulaGoal: Find the point that is located halfway between two points.

),( 11 yx

),( 22 yx

Midpoint:

Example 1Find the midpoint for the two points: (-2, 5) and (6, 1).

Midpoint:

Example 2Find the point that is ¼ of the distance from (2, 7) to (8, 3).

7

3

2 8

Example 3

Every parallelogram has diagonals that bisect each other.

Where should point S be located so that PQRS is a parallelogram?

P(-5,-4)

Q(-2,6)R(11,7)

S(x,y)