Chapter 8: Q18. (page 414)

Triangle MNP has vertices $M (3, 5), N (- 2, 8) and P (7, - 4)$ . Find the coordinates of midpoint of each side.

Short Answer

Expert verified

The coordinates of midpoint of the line segment are MN, NPand PMrespectively are $(\frac{1}{2}, \frac{13}{2}), (2.5, 2) and (5, 0.5)$ respectively.

Step by step solution

Step 1. Write down the given information.

The given line segment with end-points has coordinates $(4.3, - 2.1) and (1.9, 7.5)$ .

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 given triangle MNP has vertices $M (3, 5), N (- 2, 8) and P (7, - 4)$ .

\begin{matrix} Midpointof M N = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ = (\frac{3 - 2}{2}, \frac{5 + 8}{2}) \\ = (\frac{1}{2}, \frac{13}{2}) \end{matrix}

\begin{matrix} Midpointof N P = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ = (\frac{- 2 + 7}{2}, \frac{8 - 4}{2}) \\ = (\frac{5}{2}, \frac{4}{2}) \\ = (2.5, 2) \end{matrix}

\begin{matrix} Midpointof P M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ = (\frac{7 + 3}{2}, \frac{- 4 + 5}{2}) \\ = (\frac{10}{2}, \frac{1}{2}) \\ = (5, 0.5) \end{matrix}

Step 4. Conclusion.

The coordinates of midpoint of the line segment are MN, NPand PMrespectively are $(\frac{1}{2}, \frac{13}{2}), (2.5, 2) and (5, 0.5)$ respectively.

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Triangle MNP has vertices $M (3, 5), N (- 2, 8) and P (7, - 4)$ . Find the coordinates of midpoint of each side.

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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Triangle MNP has vertices M3,5,N-2,8andP7,-4. Find the coordinates of midpoint of each side.

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

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Logic and Functions

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Triangle MNP has vertices $M (3, 5), N (- 2, 8) and P (7, - 4)$ . Find the coordinates of midpoint of each side.