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Midpoint and Distance in the Coordinate Plane

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. y. x. 0. The Coordinate Plane Review.

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Midpoint and Distance in the Coordinate Plane

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  1. 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.

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

  3. y x 0 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) (-1, -2) (-3, 2) (2, -2) Chapter 1

  4. 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(x1, y1) and B(x2, y2) has these coordinates: Example: Find the midpoint of A (-1, 4) & B (3, 5). Chapter 1

  5. Distance Formula • In the coordinate plane, the formula for the distance between the points A(x1, y1) and B(x2, y2) is: • Example: Find AB; A(-1,3) and B(3,-2) A B Chapter 1

  6. Lesson Quiz • Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N (8, 0). • K is the midpoint of HL. H has coordinates (1, –7), and K has coordinates (9, 3). Find the coordinates of the other endpoint. • Find the distance, to the nearest tenth, between S(6, 5) and T(–3, –4). (3, 3) (17, 13) 12.7 Chapter 1

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