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Q. 55

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Precalculus Enhanced with Graphing Utilities

Found in: Page 15

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Find the midpoint of the line segment joining the points P₁ and P₂ .
$P_{1} = (3, - 4); P_{2} = (5, 4)$

The midpoint of line segment is (4,0).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Find the midpoint of the line segment joining the points P₁ and P₂ .

$P_{1} = (3, - 4); P_{2} = (5, 4)$

Step 2. Midpoint Formula.

The midpoint $M = (x, y)$ of the line segment from $P_{1} = (x_{1}, y_{1}) to P_{2} = (x_{2}, y_{2})$ is

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

Step 3. Apply the midpoint formula.

The coordinates (x, y) of the midpoint M are

$x = \frac{x_{1} + x_{2}}{2} = \frac{3 + 5}{2} = 4 and y = \frac{y_{1} + y_{2}}{2} = \frac{- 4 + 4}{2} = 0$

So, Midpoint $M = (x, y) = (4, 0)$ .

Step 4. Conclusion.

The midpoint of the line segment is $(4, 0)$ .

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