Question

segments, midpoints, & bisectors
w, r, and s are points on a number line, and w is the midpoint of $overline{rs}$. for each pair of coordinates given, find the coordinate of the third point.

1. $r = 4, s = -6$

$w = \underline{\quad\quad\quad\quad\quad\quad}$

1. $w = -4, s = 2$

$r = \underline{\quad\quad\quad\quad\quad\quad}$

Explanation:

Problem 1: Find \( W \) when \( R = 4 \) and \( S = -6 \)

Step 1: Recall midpoint formula

The midpoint \( W \) of a segment with endpoints \( R \) and \( S \) on a number line is given by \( W=\frac{R + S}{2} \).

Step 2: Substitute values

Substitute \( R = 4 \) and \( S=-6 \) into the formula: \( W=\frac{4+(-6)}{2} \).

Step 3: Simplify the expression

First, calculate the numerator: \( 4+(-6)=4 - 6=-2 \). Then, divide by 2: \( W=\frac{-2}{2}=-1 \).

Step 1: Recall midpoint formula

The midpoint formula is \( W=\frac{R + S}{2} \). We need to solve for \( R \).

Step 2: Multiply both sides by 2

Multiply both sides of the equation \( -4=\frac{R + 2}{2} \) by 2: \( -4\times2=R + 2 \), which simplifies to \( -8=R + 2 \).

Step 3: Solve for \( R \)

Subtract 2 from both sides: \( R=-8 - 2=-10 \).

Answer:

\( W=-1 \)

Problem 2: Find \( R \) when \( W = -4 \) and \( S = 2 \)