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Geometry 1-6

Geometry 1-6. Midpoint and Distance in the Coordinate Plane. Learning Targets. Students will be able to… Develop and apply the formula for midpoint. Use the distance formula to find the distance between two points. Warm-up. Find the area and the perimeter of…

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Geometry 1-6

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  1. Geometry 1-6 Midpoint and Distance in the Coordinate Plane

  2. Learning Targets • Students will be able to… • Develop and apply the formula for midpoint. • Use the distance formula to find the distance between two points.

  3. Warm-up Find the area and the perimeter of… 1. A rectangle with width 4 and length 7 2. A triangle with base 8 and height 10 Find the area and circumference of… 3. A circle with radius 4

  4. Warm-up Day 2 • Write the coordinates of the points plotted on the graph A. ___________ B. _____________ C. _____________ D. ______________

  5. Homework Check

  6. Homework Check

  7. Homework Check

  8. Homework Check

  9. Review of Vocabulary • Coordinate plane: • a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis).

  10. Review of Coordinate Planes 1. Label the graph’s x-axis and y-axis. 2. Review plotting coordinates in the form (x,y). 3. Plot points and label by the appropriate letter. H. (2,7) I. (-5, -5) J. (-3, 6) K. (1, -4) 4. Write the coordinates of the points plotted on the graph A. ____________ B. _____________ C. _____________ D. ______________

  11. Review of Coordinate Planes 1. Label the graph’s x-axis and y-axis. 2. Plot points and label by the appropriate letter. H. (4,-2) I. (-5, 0) J. (-3,6) K. (-1, -1) 3. Write the coordinates of the points plotted on the graph A. ___________ B. _____________ C. ____________ D. _____________

  12. Midpoint Formula Midpoint Formula: the midpoint M of with endpoints A and B. Formula: A B

  13. Finding the Coordinates of a Midpoint 1. Find the coordinates of the midpoint of with endpoints E(-2, 3) and F(5, -3).

  14. Finding the Coordinates of a Midpoint 2. Find the coordinates of the midpoint of with endpoints C(-2, -1) and D(4, 2).

  15. Finding the Coordinates of a Midpoint 3. Find the coordinates of the midpoint of with endpoints Y(-4, 6) and Z(3, 8).

  16. Finding the Coordinates of an Endpoint Finding the coordinates of one endpoint Steps: 1. Let the coordinates of the missing endpoint equal (x, y) 2. Use the Midpoint Formula 3. Find the x coordinate 4. Find the y coordinate 5. Rewrite the coordinates

  17. Finding the Coordinates of an Endpoint 1. M is the midpoint of A has coordinates (2, 2) and M has coordinates (4, -3). Find the coordinates of B.

  18. Finding the Coordinates of an Endpoint 2. S is the midpoint of R has coordinates (-6, -1) and S has coordinates (-1, 1). Find the coordinates of T.

  19. Finding the Coordinates of an Endpoint 3. B is the midpoint of A has coordinates (-6, -2) and B has coordinates (9, 3). Find the coordinates of C.

  20. Finding the Coordinates of an Endpoint 4. Y is the midpoint of B has coordinates (-4, -4) and Y has coordinates (-2, 3). Find the coordinates of A.

  21. Review of Square Roots • What is a square root? What does it mean? • You are looking for a number times itself that will give you the value under the square root. • How can we calculate it using a calculator? • Type 2nd button and then square root Let’s find it on everyone’s calculator. Then type the number you are looking for the square root of.

  22. Review of Square Roots • What is • What is • Why is rounding important?

  23. Distance Formula • Distance Formula: • In a coordinate plane, the distance d between two points and is

  24. Distance Formula 1. Find XY using the distance formula. X(-2, 4) and Y(6, 1).

  25. Distance Formula 2. Find EF using the distance formula. E(-2, 1) and F(-5, 5).

  26. Distance Formula 3. Find XY using the distance formula. X(5, 10) and Y(-5, -10).

  27. Review • What is the midpoint formula? • What is the distance formula?

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