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Q. 55

Expert-verified
Found in: Page 15

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Find the midpoint of the line segment joining the points P1 and P2 .${P}_{1}=\left(3,-4\right);{P}_{2}=\left(5,4\right)$

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

See the step by step solution

## Step 1. Given information.

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

${P}_{1}=\left(3,-4\right);{P}_{2}=\left(5,4\right)$

## Step 2. Midpoint Formula.

The midpoint $M=\left(x,y\right)$ of the line segment from ${P}_{1}=\left({x}_{1},{y}_{1}\right)\mathrm{to}{P}_{2}=\left({x}_{2},{y}_{2}\right)$ is

$M=\left(x,y\right)=\left(\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{2}+{y}_{1}}{2}\right)$

## Step 3. Apply the midpoint formula.

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

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

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

## Step 4. Conclusion.

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