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Q17.

Expert-verified
Found in: Page 414

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# Find the midpoint of line segment with endpoints at given coordinates $\left(\frac{1}{3},\frac{3}{4}\right)\text{and}\left(-\frac{1}{4},-\frac{1}{2}\right)$.

The coordinates of midpoint of the line segment are $\left(\frac{1}{24},\frac{1}{8}\right)$.

See the step by step solution

## Step 1. Write down the given information.

The given line segment with end-points has coordinates $\left(\frac{1}{3},\frac{3}{4}\right)\text{and}\left(-\frac{1}{4},-\frac{1}{2}\right)$.

## Step 2. Concept used.

If a line segment has end-points at $\left({x}_{1},{y}_{1}\right)\text{and}\left({x}_{2},{y}_{2}\right)$ then the midpoint of the segment has coordinates $\left(\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2}\right)$.

## Step 3. Calculation.

The coordinates of the midpoint are evaluated using the points $\left(\frac{1}{3},\frac{3}{4}\right)\text{and}\left(-\frac{1}{4},-\frac{1}{2}\right)$.

$\begin{array}{c}\text{Midpoint}=\left(\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2}\right)\\ =\left(\frac{\frac{1}{3}-\frac{1}{4}}{2},\frac{\frac{3}{4}-\frac{1}{2}}{2}\right)\\ =\left(\frac{1}{6}-\frac{1}{8},\frac{3}{8}-\frac{1}{4}\right)\\ =\left(\frac{4-3}{24},\frac{3-2}{8}\right)\\ =\left(\frac{1}{24},\frac{1}{8}\right)\end{array}$

## Step 4. Conclusion.

The coordinates of midpoint of the line segment are $\left(\frac{1}{24},\frac{1}{8}\right)$.