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Distance and Midpoints

Distance and Midpoints. Objective: (1)To find the distance between two points (2) To find the midpoint of a segment. Definitions. Midpoint: The points halfway between the endpoints of a segment.

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Distance and Midpoints

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  1. Distance and Midpoints Objective: (1)To find the distance between two points(2) To find the midpoint of a segment

  2. Definitions • Midpoint: The points halfway between the endpoints of a segment. • Distance Formula: A formula used to find the distance between two points on a coordinate plane. • Segment Bisector: A segment, line, or plane that intersects a segment at its midpoint.

  3. -6 -4 -2 0 2 6 8 10 12 Midpoint • To find the midpoint along the number line, add both numbers and divide by 2. A B C D E F G H I J 4 Find the midpoint of BH The coordinate of the midpoint is 2. E is the midpoint.

  4. More Midpoint B(-1,7) • For the midpoint on a coordinate plane, the formula is: A(-8,1) This is the midpoint.

  5. Finding the endpoint of a segment • Find the coordinates for X if M(5,-1) is the midpoint and the other endpoint has coordinates Y(8,-3) • helps us find the x-coordinate of the endpoint. • We’re still going to use the Midpoint Formula: • But the there will be a few unknowns:

  6. Finding the endpoint of a segment Multiply both sides by 2 to eliminate the denominator -8 -8 Subtract 8 from both sides x2 = 2 This is the x-coordinate of the other endpoint This helps us find the y-coordinate of the midpoint

  7. Finding the endpoint of a segment +3 +3 y2 = 1 This is the y-coordinate of the endpoint The coordinate of the other endpoint is X(2,1).

  8. M is the midpoint of AB. Find the value of x: Since M is a midpoint, that means that AM=MB which means 3x – 5 = x + 9 -x -x 2x – 5 = 9 +5 +5 2x = 14    Finding the value of a variable A 3x - 5 M x + 9 B • 2x = 14 • 2 • x = 7

  9. Remember: AB means the length of AB To find the distance on the number line, take the absolute value of the difference of the coordinates. a – b -6 -4 -2 0 2 4 6 8 10 12 Distance A B C D E F G H I J Find CJ -2 -12=-14= 14 CJ = 14 Find EA 2 – (-6) =2+6 =8 = 8 EA = 8

  10. A(-3,1) B(4,-2) More Distance The distance between two points in the coordinate plane is found by using the following formula:

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