P.5 The Cartesian Plane Our goals are to learn

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Presentation transcript:

P.5 The Cartesian Plane Our goals are to learn How to plot points in the Cartesian Plane Use the distance formula to find the distance between two points. Use the Midpoint formula to find the midpoint of a line segment.

The Cartesian Plane An ordered pair is . . . a pair of two real numbers x and y, written (x, y), which represents a point in the Cartesian plane.

Examples Plot the ordered pairs on the coordinate plane. (4, -2), (0, 0), (-4, 0), (-5, -5)

Example Find the coordinates of the point The point is located three units below the x-axis and two units to the right of the y-axis. The point is on the x-axis and 10 units to the left of the y-axis.

x<0 and y<0 x = -4 and y > 0 x > 4 -x > 0 and y < 0 Example Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. x<0 and y<0 x = -4 and y > 0 x > 4 -x > 0 and y < 0 xy < 0

Use the distance formula to find the length of the segment. (6, -3), (6, 5) (-3, -1), (2, -1) (8, 5), (0, 20)

Examples Find the length of each side of the right triangle and show that these lengths satisfy the Pythagorean Theorem.

Examples Show that the points form the vertices of the polygon Parallelogram: (0, 1), (3, 7), (4, 4), (1, -2)

Use the midpoint formula to find the center of the segment. (6, -3), (6, 5) (-3, -1), (2, -1) (8, 5), (0, 20)