Question

given coordinates p = -15, q = -12, r = 0, s = 3, and t = 7, find each answer using the number line.

1. find ps.
2. find the coordinate of the midpoint of ps.
3. name a segment on the number line that is congruent to pq.
4. if t is the midpoint of qv, then find the coordinate of v.
5. use the segment addition postulate to complete: pq + qr = ______.

Explanation:

Step1: Calculate the length of PS

The distance between two points on a number - line is given by the absolute value of the difference of their coordinates. For points $P=-15$ and $S = 3$, $PS=\vert S - P\vert=\vert3-(-15)\vert=\vert3 + 15\vert=18$.

Step2: Find the mid - point of PS

The mid - point $M$ of two points with coordinates $x_1$ and $x_2$ on a number line is given by $M=\frac{x_1 + x_2}{2}$. For $P=-15$ and $S = 3$, the mid - point is $\frac{-15 + 3}{2}=\frac{-12}{2}=-6$.

Step3: Find a congruent segment to PQ

First, find the length of $PQ$. $PQ=\vert Q - P\vert=\vert-12-(-15)\vert=\vert-12 + 15\vert = 3$. The segment $RS$ has length $RS=\vert S - R\vert=\vert3-0\vert = 3$. So $RS$ is congruent to $PQ$.

Step4: Find the coordinate of V if T is the mid - point of QV

Let the coordinate of $V$ be $x$. The mid - point formula for two points $Q=-12$ and $V=x$ with mid - point $T = 7$ is $\frac{Q+V}{2}=T$. Substituting the values, we get $\frac{-12 + x}{2}=7$. Multiply both sides by 2: $-12+x = 14$. Then add 12 to both sides: $x=26$.

Step5: Apply the Segment Addition Postulate

The Segment Addition Postulate states that if $Q$ is between $P$ and $R$, then $PQ+QR=PR$. The length of $PR=\vert R - P\vert=\vert0-(-15)\vert = 15$.

Answer:

1. 18
2. -6
3. $RS$
4. 26
5. $PR$