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Understanding Distance and Midpoint in Coordinate Geometry

This resource focuses on key concepts of distance and midpoint within coordinate geometry. It includes explanations about points on a coordinate plane, formulas for calculating midpoints and distances, and practical applications in finding the area and perimeter of shapes. Featured are various exercises where students will practice calculating midpoints between points, determining distances, and applying these concepts to area and perimeter equations. Ideal for reinforcing geometry skills through hands-on practice and problem-solving.

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Understanding Distance and Midpoint in Coordinate Geometry

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  1. Midpointand Distance May 6th,2013

  2. Warm Up • Solve for x. −5(1 − 5x) + 5(−8x− 2) = −4x − 8x 2. Factor. z2 - z - 3 = 0 3. Factor. 2x2 + 7x + 3

  3. Vocabulary • Distance: is a numerical description of how far apart two points are • Midpoint: divides a segment into two congruent pieces

  4. Points on a Coordinate Plane • What is a point? • How do you show a point’s location on the coordinate plane? • What comes first? A(x1, y1) B(x2, y2)

  5. Midpoint FORMULA • Number Line: • Coordinate Plane:

  6. Example • Calculate the midpoint of segment EB.

  7. You TryFind the Midpoint • L(0, 0), M(9, 3)

  8. You Try!Find the Midpoint 2 and 7

  9. Find the midpoint between C and D

  10. Distance Formula • Number Line: • Coordinate Plane:

  11. Example • Calculate the distance between D and A.

  12. You tryFind the distance • K(0, 5), L(7, 9)

  13. You Try Find the distance between C and D

  14. Finding Area and Perimeter • Use the distance formula to find the “area” and “perimeter” • The area for a square/rectangle is A = b•h • The area for a triangle is A = ½ b•h • For perimeter you ADD UP the distance of all the sides of the shape.

  15. Find the Area and Perimeter of Triangle RPQ .

  16. You Try • Find the area of the shape below.

  17. Find the Perimeter

  18. Homework Worksheet 1-7 Evens

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