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Q17.

Expert-verified

Algebra 2

Found in: Page 414

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Find the midpoint of line segment with endpoints at given coordinates $(\frac{1}{3}, \frac{3}{4}) and (- \frac{1}{4}, - \frac{1}{2})$ .

The coordinates of midpoint of the line segment are $(\frac{1}{24}, \frac{1}{8})$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given information.

The given line segment with end-points has coordinates $(\frac{1}{3}, \frac{3}{4}) and (- \frac{1}{4}, - \frac{1}{2})$ .

Step 2. Concept used.

If a line segment has end-points at $(x_{1}, y_{1}) and (x_{2}, y_{2})$ then the midpoint of the segment has coordinates $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .

Step 3. Calculation.

The coordinates of the midpoint are evaluated using the points $(\frac{1}{3}, \frac{3}{4}) and (- \frac{1}{4}, - \frac{1}{2})$ .

$\begin{matrix} Midpoint = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ = (\frac{\frac{1}{3} - \frac{1}{4}}{2}, \frac{\frac{3}{4} - \frac{1}{2}}{2}) \\ = (\frac{1}{6} - \frac{1}{8}, \frac{3}{8} - \frac{1}{4}) \\ = (\frac{4 - 3}{24}, \frac{3 - 2}{8}) \\ = (\frac{1}{24}, \frac{1}{8}) \end{matrix}$

Step 4. Conclusion.

The coordinates of midpoint of the line segment are $(\frac{1}{24}, \frac{1}{8})$ .

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