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Q. 42

Expert-verifiedFound in: Page 15

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Find the distance $d({P}_{1},{P}_{2})$ between the points ${P}_{1}\mathrm{and}{P}_{2}$.

${P}_{1}=(-4,-3);{P}_{2}=(6,2)$

The distance between the points is $d=5\sqrt{5}$.

Find the distance between the points.${P}_{1}=(-4,-3);{P}_{2}=(6,2)$

The length of the line segment is the distance between the points ${P}_{1}=({x}_{1},{y}_{1})=(-4,-3)\mathrm{and}{P}_{2}=({x}_{2},{y}_{2})=(6,2)$. Using the distance formula with${x}_{1}=-4,{y}_{1}=-3,{x}_{2}=6,\mathrm{and}{y}_{2}=2$, the length d is

$d=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{({y}_{2}-{y}_{2})}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{{\left(6-(-4)\right)}^{2}+{(2-(-3\left)\right)}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{{\left(10\right)}^{2}+{\left(5\right)}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{100+25}\phantom{\rule{0ex}{0ex}}d=\sqrt{125}\phantom{\rule{0ex}{0ex}}d=5\sqrt{5}$

The distance between the points is $5\sqrt{5}$.

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