2.1 Coordinate Plane

 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 y x

Distance Formula

y A v d h B x Point A has coordinates: Point B has coordinates: (

x

1 ,

y

1 ) (

x

2 ,

y

2 ) Vertical distance, v, is Horizontal distance, h, is

Distance Formula(continued)

y A d v B h x Since we are dealing with a right triangle: And: So, given any two points, you can find the distance between them.

Example 1

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

First, draw both points and make a guess.

Example 2

Find 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) Need both distances to equal.

(4,-2)

Midpoint Formula

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

(

x

1 ,

y

1 ) (

x

2 ,

y

2 ) Midpoint:

Example 1

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

Midpoint:

Example 2

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

7 3 2 8

Example 3

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

Every parallelogram has diagonals that bisect each other.

R(11,7) Q(-2,6) P(-5,-4) S(x,y)