Question

1 - 2 line segments and distance

1. xq = 13, xp = 5x - 3, pq = 40

find the value of the variable and xp, if x is between p and q

1. xq = 3k, xp = 7k - 2, pq = 8k + 16
2. name a point that is not contained in any of the three lines a, b, or c.
3. give another name for plane wpk.
4. name the geometric term that is best modeled by each item.

Explanation:

Step1: Use segment - addition postulate

Since X is between P and Q, $PQ=XP + XQ$.

Step2: Substitute the given expressions

$40=(5x - 3)+13$.

Step3: Simplify the right - hand side

$40 = 5x+10$.

Step4: Solve for x

$5x=30$, so $x = 6$.

Step5: Find XP

$XP=5x - 3=5\times6 - 3=27$.

Answer:

$x = 6$, $XP = 27$