Chapter 8: Q17. (page 414)

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

Short Answer

Expert verified

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

Step by step solution

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

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

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Find the midpoint of line segment with endpoints at given coordinates 13,34and-14,-12.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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