Q21. Find the coordinates of the midp... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q21. (page 661)

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

Short Answer

Expert verified

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

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:

$(x, y) = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 鈥� (1)$

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

Step 2. Calculate the distance.

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

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

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

Step 3. State the conclusion.

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

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91影视

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

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.

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91影视

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

Geometry

Decision Maths

Pure Maths

Statistics

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

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