Question

Find the value of x and the length of each segment using the segment addition postulate.

Point A is between points S and K.
The points are collinear.
SA = x-5
AK = x-3
SK = 10
SA =?
AK =?

Answer 1

The value of x is found to be 9 by using the Segment Addition Postulate. Consequently, the lengths of segment SA and AK are determined to be 4 units and 6 units, respectively.

Step-by-step explanation:

Using the Segment Addition Postulate, which states that if point A is between points S and K, then SA + AK = SK, we can set up the equation (x - 5) + (x - 3) = 10 to find the value of x and subsequently the lengths of each segment, SA and AK.

1. Solve for x: (x - 5) + (x - 3) = 10
2. Combine like terms: 2x - 8 = 10
3. Add 8 to both sides of the equation: 2x = 18
4. Divide both sides by 2 to find x: x = 9
5. Find SA: SA = x - 5 = 9 - 5 = 4
6. Find AK: AK = x - 3 = 9 - 3 = 6

Hence, the length of segment SA is 4 units and the length of segment AK is 6 units.