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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 3: Q38. (page 113)

Find the coordinates of the midpoint of $\bar{A B}$ . (You may want to draw an diagram.)
$A (- 3, 4)$ , $B (- 3, - 4)$ .

Short Answer

Expert verified

The coordinates of the midpoint of $\bar{A B}$ isrole="math" localid="1647366699895" $(- 3, 0)$ .

Step by step solution

01

Step 1. Write the formula to find the coordinates of the midpoint of the line joining the points Ax1,y1and Bx2,y2.

The formula to find the coordinates of the midpoint of the line joining the points $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ is $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .

02

Step 2. Find the coordinates of the midpoint of the line joining the points A(-3,4) and B(-3,-4).

The coordinates of the midpoint of the line joining the points $A (- 3, 4)$ and $B (- 3, - 4)$ is given by:

$\begin{matrix} (\frac{- 3 + (- 3)}{2}, \frac{4 + (- 4)}{2}) = (\frac{- 3 - 3}{2}, \frac{4 - 4}{2}) \\ = (\frac{- 6}{2}, \frac{0}{2}) \\ = (- 3, 0) \end{matrix}$

03

Step 3. Write the conclusion.

The coordinates of the midpoint of the line joining the points $A (- 3, 4)$ and $B (- 3, - 4)$ is $(- 3, 0)$ .

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