1310_1o1_notes - Math 1310 1.1 Points Regions Distance and Midpoints Section 1.1 Points Regions Distance and Midpoints A point P in the coordinate plane

1310_1o1_notes - Math 1310 1.1 Points Regions Distance and...

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Math 1310 1.1 Points, Regions, Distance and Midpoints 1 Section 1.1 - Points, Regions, Distance and Midpoints A point P in the coordinate plane is located by a unique ordered pair of numbers (a,bThe number a is called the x-coordinate and b is called the y-coordinate Example:Plot the following points: (0, 0), (1, 0), (0, 3), (-2, 3), (0, -1), (4, -3), (-1, -4) ). of P .
Math 1310 1.1 Points, Regions, Distance and Midpoints 2 Regions The set of all points in the coordinate plane with y-coordinate k is the horizontal line y k. The set of all points in the coordinate plane with x-coordinate k is the vertical line x k. Example: Graph : 4 y (same as {( x , y ) : y 4} ) Example: Graph: 4 y
Math 1310 1.1 Points, Regions, Distance and Midpoints 3 Example: Graph: 1 x Example: Graph: 1 2 x
Math 1310 1.1 Points, Regions, Distance and Midpoints 4 Example: Graph: x , 2 y Distance The distance between two points ) , ( 1 1 y x A and ) , ( 2 2 y x B in the plane is given by 2 1 2 2 1 2 ) ( ) ( ) , ( y y x x B A d
Math 1310 1.1 Points, Regions, Distance and Midpoints 5 Example: Find the distance between the points (-4, 5) and (3, 2). Midpoint The midpoint of the line segment that connects two points ) , ( 1 1 y x A and ) , ( 2 2 y x B in the plane is given by 2 , 2 2 1 2 1 y y x x Example: Find the midpoint of the line segment from (5, -4) and (3, 2).
Math 1310 1.1 Points, Regions, Distance and Midpoints 6 Example: Find the midpoint of the line segment from (-4, -3) and (2, 2).

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