Coordinate Plane: Basics and Formulas

1. The coordinate plane is formed by the intersection of two perpendicular number lines called axes. The point of intersection, called the origin, is at 0 on each number line. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis.

2. Reading Math The x-coordinate tells how many units to move left or right from the origin. The y-coordinate tells how many units to move up or down. Points on the coordinate plane are described using ordered pairs. An ordered pair consists of an x-coordinate and a y-coordinate and is written (x, y). Points are often named by a capital letter.

3. U(0, –5) • Example 1: Graphing Points in the Coordinate Plane Graph each point. A. T(–4, 4) Start at the origin. T(–4, 4) • Move 4 units left and 4 units up. B. U(0, –5) Start at the origin. Move 5 units down. • C. V (–2, –3) V(–2, −3) Start at the origin. Move 2 units left and 3 units down.

4. Midpoint and Distance in the Coordinate Plane • You can use formulas to find the midpoint and the length of any segment in the coordinate plane. Number Line Coordinate Plane

5. Finding the Midpoint • Segment AB has endpoints at -4 and 9. What is the coordinate of its midpoint?

6. Finding the Midpoint • Segment EF has endpoints E (7 , 5) and F (2 , -4). What are the coordinates of its midpoint M?

7. Finding an Endpoint • The midpoint of segment CD is M(-2 , 1). One endpoint is C (-5 , 7). What are the coordinates if the other endpoint D?

8. Distance Formula • The distance between two points A(x1 , y1) and B(x1 , y1) is

9. Finding Distance • What is the distance between U(-7 , 5) and V(4 , -3)? Round to the nearest tenth?

10. Practice • Page 56 1-9, 18-23