1.3 PowerPoint.pptx - 1.3 Key Midpoint The Point that...

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1.3 Key Concepts
Midpoint The Point that divides the segment into two congruent segments.
Segment Bisector A Point, Ray, Line, Line Segment, or Plane that intersects the segment at its Midpoint
Midpoint Formula [(x 1 + x 2 )/2] , [(y 1 + y 2 )/2]
Distance Formula AB = √[(x 2 -x 1 ) 2 + (y 2 - y 1 ) 2 ]
In the skateboard design, VW bisects XY at point T , and XT = 39.9 cm . Find XY . Skateboard SOLUTION EXAMPLE 1 Find segment lengths Point T is the midpoint of XY . So , XT = TY = 39.9 cm . XY = XT + TY = 39.9 + 39.9 = 79.8 cm Segment Addition Postulate Substitute. Add.
SOLUTION EXAMPLE 2 Use algebra with segment lengths STEP 1 Write and solve an equation. Use the fact that VM = MW . VM = MW 4 x 1 = 3 x + 3 x – 1 = 3 x = 4 Write equation. Substitute. Subtract 3 x from each side. Add 1 to each side. Point M is the midpoint of VW . Find the length of VM . ALGEBRA
EXAMPLE 2 Use algebra with segment lengths STEP 2 Evaluate the expression for VM when x = 4 . VM = 4 x – 1 = 4(4) – 1 = 15 So, the length of VM is 15. Check: Because VM = MW , the length of MW should be 15 . If you evaluate the expression for MW , you should find that MW = 15 .
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