# Midpoint and Distance in the Coordinate Plane SEI

- Slides: 6

Midpoint and Distance in the Coordinate Plane SEI. 3. AC. 4: Use, with and without appropriate technology, coordinate geometry to represent and solve problems including midpoint, length of a line segment and Pythagorean Theorem. FHS Chapter 1

The Coordinate Plane Review • The coordinate plane is y a plane divided into 4 regions by the x-axis II I and the y-axis. • These 4 areas are called 0 quadrants. III IV • Here are the four quadrants: • The 0 in the center is called the origin. FHS Chapter 1 x 2

Graphing Points Review • The location, or coordinates, of a point are given by an ordered pair (x, y) • The first number tells us to go right or left and the second number tells us to go up or down. • Let’s look at some examples: (2, 3) (-3, 2) (-1, -2) (2, -2) FHS Chapter 1 y x 0 3

Midpoint Formula • You can find the midpoint of a segment by using the coordinates of its endpoints. • The midpoint of the segment joining the points A(x 1, y 1) and B(x 2, y 2) has these coordinates: Example: Find the midpoint of A (-1, 4) & B (3, 5). FHS Chapter 1 4

Distance Formula • In the coordinate plane, the formula for the distance between the points A(x 1, y 1) and B(x 2, y 2) is: • Example: Find AB; A(-1, 3) and B(3, -2) A B FHS Chapter 1 5

Lesson Quiz 1. Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N (8, 0). (3, 3) 2. K is the midpoint of HL. H has coordinates (1, – 7), and K has coordinates (9, 3). Find the coordinates of the other endpoint. (17, 13) 3. Find the distance, to the nearest tenth, between S(6, 5) and T(– 3, – 4). 12. 7 FHS Chapter 1 6