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Chapter 8: Q10. (page 414)

Find the midpoint of line segment with endpoints at given coordinates ( 8,3) and ( 16,7 ).

Short Answer

Expert verified

The coordinates of midpoint of the line segment are $(12, 5)$ .

Step by step solution

01

Step 1. Write down the given information.

The given line segment with end-points has coordinates $(8, 3) and (16, 7)$ .

02

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 $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .

03

Step 3. Calculation.

The coordinates of the midpoint are evaluated using the points $(8, 3) and (16, 7)$ .

\begin{matrix} Midpoint = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ = (\frac{8 + 16}{2}, \frac{3 + 7}{2}) \\ = (\frac{24}{2}, \frac{10}{2}) \\ = (12, 5) \end{matrix}

04

Step 4. Conclusion.

The coordinates of midpoint of the line segment are $(12, 5)$ .

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