Equation Practice With Segment Addition
Segment addition postulate
The segment add-on postulate states the post-obit for 3 points that are collinear.
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If 3 points A, B, and C are collinear and B is between A and C, then
AB + BC = Air conditioning
Using the segment addition postulate to solve a problem.
Suppose Air-conditioning = 48, find the value of x. Then, observe the length of AB and the length of BC.
AB + BC = Air-conditioning
( 2x - iv ) + ( 3x + 2 ) = 48
2x + 3x - 4 + 2 = 48
5x - 4 + ii = 48
Add 4 to both sides of the equation.
5x - 4 + 4 + ii = 48 + iv
5x + ii = 52
Decrease 2 from both sides.
5x + 2 - 2 = 52 - two
5x = 50
Split up both sides by v
5x / v = 50 / 5
x = ten
Now that nosotros have the value of x, we can find the length of AB and the length of BC.
AB = 2x - iv
AB = 2 × ten - 4
AB = 20 - iv = 16
The length of AB is 16
BC = 3x + 2
BC = 3 × 10 + 2
BC = thirty + 2 = 32
The length of BC is 32.
Segment addition postulate and the midpoint
Suppose XA = 3x and AY = 4x - half-dozen. If A is the midpoint of XY, what is the length of XY?
3x 4x - 6
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X A Y
The trick in this problem is to come across that if A is the midpoint, then XA = AY.
Since XA = AY, 3x = 4x - half dozen
Subtract 3x from both sides.
3x - 3x = 4x - 3x - six
0 = x - 6
Add 6 to both sides of the equation.
0 + half-dozen = 10 - 6 + vi
6 = x
To compute XA, you tin can either use 3x or 4x - six
Using 3x, nosotros get XA = AY = three × 6 = 16
Using 4x - 6, nosotros get XA = AY = 3 × 6 - six = xviii - 6 = 12
XY = XA + AY = 16 + xvi = 32
The length of XY is 32.
Equation Practice With Segment Addition,
Source: https://www.basic-mathematics.com/segment-addition-postulate.html
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