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Q. 47

Expert-verified
Found in: Page 15

### Precalculus Enhanced with Graphing Utilities

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

# Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.

The length of line segment is $2\sqrt{65}$.

See the step by step solution

## Step 1. Given information.

Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.

## Step 2. locate the coordinates of end points of line segment.

Looking at the x-axis, it can be said that every tick is equal to 2 from having 6 marks with 12 and -12 being the 6th marks on both ends. On the other hand, on y-axis, every tick is equal to 2 because of the 6 marks and 12 and -12 being the 6th marks.

The first point from right to left is 4 units to the left and 6 units above the origin. Thus, (-4, 6) = (x1, y1) .

The second point is 4 units to the right and 8 units above the origin. Thus, (4, -8) = (x2, y2) .

## Step 3. Substitute the values in the distance formula.

The length of the line segment is the distance between the points $\left({x}_{1},{y}_{1}\right)=\left(-4,6\right)\mathrm{and}\left({x}_{2},{y}_{2}\right)=\left(4,-8\right)$.

Using the distance formula the length d is

$d=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{2}\right)}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{{\left(4-\left(-4\right)\right)}^{2}+{\left(-8-6\right)}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{{\left(8\right)}^{2}+{\left(-14\right)}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{64+196}\phantom{\rule{0ex}{0ex}}d=\sqrt{260}\phantom{\rule{0ex}{0ex}}d=2\sqrt{65}$

## Step 4. Conclusion.

The length of line segment is $2\sqrt{65}$.