The segment addition postulate states the following for 3 points that are collinear.

If 3 points A, B, and C are collinear and B is between A and C, then
AB + BC = AC
Suppose AC = 48, find the value of x. Then, find AB and BC
AB + BC = AC
( 2x  4 ) +( 3x + 2 ) = 48
2x + 3x  4 + 2 = 48
5x  4 + 2 = 48
Add 4 to both sides of the equation
5x  4 + 4 + 2 = 48 + 4
5x + 2 = 52
Subtract 2 from both sides
5x + 2  2 = 52  2
5x = 50
Divide both sides by 5
5x / 5 = 50 / 5
x = 10
AB = 2x  4
AB = 2 × 10  4
AB = 20  4 = 16
BC = 3x + 2
BC = 3 × 10 + 2
BC = 30 + 2 = 32
Suppose XA = 3x and AY = 4x  6. If A is the midpoint of XY, what is the length of XY?
3x 4x  6
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X A Y
If A is the midpoint, XA = AY.
3x = 4x  6
Subtract 3x from both sides
3x  3x = 4x  3x  6
0 = x  6
Add 6 to both sides of the equation
0 + 6 = x  6 + 6
6 = x
XA = AY = 3 × 6 = 16
XY = XA + AY = 16 + 16 = 32
Mar 13, 19 11:50 AM
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Learn how to derive the equation of an ellipse when the center of the ellipse is at the origin.