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Understanding Midpoints, Segment Bisectors, and Distance in Coordinate Geometry

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This lesson explores the concepts of midpoints, segment bisectors, and the distance formula in coordinate geometry. Learn how to find the midpoint of a segment by averaging the x and y coordinates of its endpoints. Apply the segment bisector concept in real-world problems, such as skateboard design. Additionally, discover how to calculate the distance between two points in a coordinate plane. Through examples and practice problems, deepen your understanding of these essential geometric principles.

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Understanding Midpoints, Segment Bisectors, and Distance in Coordinate Geometry

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  1. Lesson 1.3 Midpoint and distance

  2. midpoint • The midpoint of a segment is the point that divides the segment into two congruent segments.

  3. Segment Bisector • Examples C B B M M A A D

  4. The Real World • In the skateboard design, bisects at point T, and XT = 39.9 cm. Find XY and state postulate used.

  5. Indy Practice • Find the length of VW 4x-1 3x+3 M

  6. Midpoint Formula Use coordinates of endpoints to find midpoint The coordinates of the midpoint of a segment are the averages of the x-coordinates and y-coordinates

  7. Coordinate Plane • Plot A (x1, x2) and B (y1, y2) and find coordinates of the midpoint of AB

  8. Example • The endpoints of RS are R(1, -3) and S(4, 2). Find the coordinates of midpoint M.

  9. Indy Practice • M(2, 1) of . One of the endpoints is J(1, 4). Find K

  10. Distance Formula • Find the distance between 2 points in a coordinate plane. • Plot A (x1, x2) and B (y1, y2)

  11. Derive the Distance Formula

  12. Example • Find the distance between R(2, 3) and S(4, -1)

  13. Indy Practice • Find the distance between P(1, 2) and Q(5, 4)

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