Chapter 10: Q21. (page 661)

Find the coordinates of the midpoint of the segment with the given endpoints.
$(- 3, 4), (- 2, - 3)$

Short Answer

Expert verified

The coordinates of the midpoint of the segment with the given endpoints is $(- \frac{5}{2}, \frac{1}{2})$ .

Step by step solution

Step 1. State the concept of ‘midpoint of a segment in 2 dimensional plane’.

Let the two points in 2 dimensional plane be $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

The midpoint of the segment with endpoints is given as:

$(x, y) = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \dots (1)$

Where $(x, y)$ is the midpoint.

Step 2. Calculate the distance.

The two points which is given are $(- 3, 4)$ and $(- 2, - 3)$ .

Substitute $(- 3, 4)$ as $(x_{1}, y_{1})$ and $(- 2, - 3)$ as $(x_{2}, y_{2})$ in $(1)$ to calculate the distance.

role="math" localid="1647928515911" $\begin{array}{l} (x, y) = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ = (\frac{- 3 + (- 2)}{2}, \frac{4 + (- 3)}{2}) \\ = (\frac{- 3 - 2}{2}, \frac{4 - 3}{2}) \\ = (\frac{- 5}{2}, \frac{1}{2}) \\ = (- \frac{5}{2}, \frac{1}{2}) \end{array}$

Step 3. State the conclusion.

Therefore, midpoint of the segment with the endpoints $(- 3, 4)$ and $(- 2, - 3)$ is $(- \frac{5}{2}, \frac{1}{2})$ .

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Find the coordinates of the midpoint of the segment with the given endpoints.
$(- 3, 4), (- 2, - 3)$

Short Answer

Step by step solution

Step 1. State the concept of ‘midpoint of a segment in 2 dimensional plane’.

Step 2. Calculate the distance.

Step 3. State the conclusion.

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Find the coordinates of the midpoint of the segment with the given endpoints.(−3,4), (−2,−3)

Short Answer

Step by step solution

Step 1. State the concept of ‘midpoint of a segment in 2 dimensional plane’.

Step 2. Calculate the distance.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Decision Maths

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Find the coordinates of the midpoint of the segment with the given endpoints.
$(- 3, 4), (- 2, - 3)$