1. 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

2. Distance Formula x y A B Point A has coordinates: Point B has coordinates: Vertical distance, v, is Horizontal distance, h, is d v h

3. 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.

4. Example 1 Find the distance between (5, 4) and (2, -1). First, draw both points and make a guess.

5. 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

6. Example 2(continued) (1,2) (4,-2) Need both distances to equal.

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

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

9. Example 2 Find the point that is ¼ of the distance from (2, 7) to (8, 3). 7 3 28

10. 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)