Understanding the Midpoint of a Line Segment

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Explore how to find the midpoint of a line segment through visual aids and practice exercises. Learn the formula for calculating the midpoint between two points on a line. Key points highlight the importance of averaging x and y coordinates. Start mastering geometric concepts with this comprehensive resource.

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The Midpoint of a Line Anne Gilleran

The Midpoint of a Line Learning Intention To learn how to find the midpoint of a line segment

The Midpoint of a Line (Warm Up) +3 + -2 = 5. +4 + -6 = -2 +1 1. -3 + -2 = 6. -5 + -7 = -12 -5 2. -3 + +1 = 7. -2 + +8 = +6 -2 3. +2 + -3 = 8. +6 + -9 = -3 -1 4.

The Midpoint of a Line What s half way between each pair of numbers? 4 ? 8.5 ? 1. 2 & 6 6. 7 & 10 6 ? -7 ? 2. 4 & 8 7. -9 & -5 16 ? -7.5 ? 3. 12 & 20 8. -10 & -5 0 ? -4 ? 4. -3 & 3 9. -11 & 3 2 ? 39 ? 5. -2 & 6 10. 28 & 50

This is a line This is a line segment

Find the midpoint of the lines between.... b. (2,6) and (5,2) a. (0,1) and (6,5) y y 5 4 3 2 1 0 5 4 3 2 1 0 x x 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Can you write a formula for co- ordinates (x1,y1) and (x2,y2) Midpoint at (3,3)

KEY POINT KEY POINT The midpoint of a line The midpoint of a segment is the average of the two x co-ordinates and two y co-ordinates. y 2 + 4 2 = (2,5) x co-ordinate: 5 + 2 2 y co-ordinate: = (4,2) x midpoint at ( , )

KEY POINT KEY POINT The midpoint of a line The midpoint of a line between points y (x1,y1) and (x2,y2) is... (x1,y1) x1+ x2 2 y1+ y2 2 , (x2,y2) x

Find the midpoint of the line segment between points (-3,2) and (2,-3) 3 2 Midpoint at 1 x1+ x2 2 y1+ y2 2 , -3 -2 -1 1 2 3 -1 -2 -3

Find the midpoint of the line segments between these sets of points (answer with plickers) (3,6) 1. (0,3) & (6,5) (6,7) 2. (2,5) & (10,9) (7,11) 3. (8,12) & (6,10) (-4,7) 4. (-3,7) & (-5,7) (3.5,6) 5. (2,2) & (5,10) (0,1) 6. (0,-3) & (0,5) (-6,25) 7. (-7,-10) & (-5,60) (-11.5,-37) 8. (-13,-81) & (-10,7)

Bonus Questions 1. Find the centre of a square with co-ordinates at A (-4,12), B (8,4), C(0,-8) & (12,0) 2. Two boats begin at the same place. One sails East at 15 nautical miles per hour, the other sails South at the same speed. After 3 hours they turn & begin sailing toward each other. Where do they meet in relation to where they first started?

Q1 ANSWER Midpoint at (-2,-2) 12 8 4 -12 -8 -4 4 8 12 -4 -8 -12

Q2 ANSWER N Meet at 22.5 nautical miles East, 22.5 nautical miles South E 15 30 45 15 30 45

PLENARY Find the midpoint of the line between (0,5) and (6,1) y Explain how to find the midpoint of a line segment in one sentence. 5 4 3 2 1 0 x 0 1 2 3 4 5 6