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Distance Formula and Midpoint Formula for Finding Points in a Plane

Learn how to use the distance formula to find the distance between two points in a plane, and how to use the midpoint formula to find the midpoint of a segment with known endpoints.

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Distance Formula and Midpoint Formula for Finding Points in a Plane

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  1. Chapter 1Section 1.3 Distance Formula Notebook Check Time

  2. Distance Formula The distance between any two point in a plane can be found by using the distance formula.

  3. Find the distance between A(1, 3) and B(-2, 4) • Write out the formula 2.Fill in the formula 3. Simplify the formula Already Simplified 4. Simplify the radical

  4. Find the distance between A(-2, 5) and B(0, 7) • Write out the formula 2.Fill in the formula 3. Simplify the formula 8 = 4 • 2 4. Simplify the radical Always simplify every radical you ever see

  5. Find the distance between A(7, -2) and B(3, 6) • Write out the formula 2.Fill in the formula 3. Simplify the formula 80 = 16 • 5 4. Simplify the radical Always simplify every radical you ever see

  6. 8.6 Continued… Distance Formula Find AB using the Pythagorean Theorem: (AB)2 = (x2 – x1)2 + (y2 – y1)2 B (x2, y2) • |y2 – y1| • C(x2, y1) A(x1, y1) |x2 – x1| This formula can be used to find the distance between any two points in the plane

  7. Find the distance between each pair of points 1. G(-1, 0), H(2, -4) Find GH

  8. Find the distance between each pair of points 2. G(-1, 0), I(1, 3) Find GI

  9. Find the distance between each pair of points 3. H(2, -4), I(1, 3) Find HI

  10. Find the distance between each pair of points 4. E(-2, 4), F(0, -4) Find EF

  11. Chapter 1Section 1.5 Segments and Angle Bisectors

  12. Midpoint • The midpoint of a segment is the point that divides the segment into two congruent segments • Bisect: • Two cut a figure in half A B C Midpoint Since B is the midpoint of , then

  13. Midpoint formula • Used to find the midpoint of a segment with known endpoints If A(x1, y1) and B(x2, y2) are the endpoints of segment AB, then the midpoint of segment AB has coordinates

  14. A(-3, 5) and B(5, -1) Use the formula C(-4, -3) and D(6, 3) Use the formula Find the coordinates of the midpoint of a segment with the given endpoints

  15. T(4, 1) and M(3, 0) Use the formula Remember the other endpoint is (x2, y2) Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint M 1. Find x2 2. Find y2 The other endpoint is (2, -1)

  16. T(-4, 3) and M(-1, -5) Use the formula Remember the other endpoint is (x2, y2) Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint M 1. Find x2 2. Find y2 The other endpoint is (2, -13)

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