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Q16.

Expert-verifiedFound in: Page 661

Book edition
Student Edition

Author(s)
Carter, Cuevas, Day, Holiday, Luchin

Pages
801 pages

ISBN
9780078884801

**Find the distance between the points with the given coordinate.**

**$\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{)}\mathbf{,}\mathbf{\text{\hspace{0.17em}}}\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{5}\mathbf{)}$**

The distance between the coordinates $(2,3)$ and $(3,5)$ is $\sqrt{5}$ **units**.

Let the two points in 2 dimensional plane be $({x}_{1},{y}_{1})$ and $({x}_{2},{y}_{2})$.

The distance between the points is given as:

$d=\sqrt{{({x}_{2}-{x}_{1})}^{2}+{({y}_{2}-{y}_{1})}^{2}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\dots \left(1\right)$

Where $d$ is the distance.

The two points which is given are $(2,3)$ and $(3,5)$.

Substitute $(2,3)$ as $({x}_{1},{y}_{1})$ and $(3,5)$ as $({x}_{2},{y}_{2})$ in $\left(1\right)$ to calculate the distance.

localid="1647926325268" $\begin{array}{l}d=\sqrt{{({x}_{2}-{x}_{1})}^{2}+{({y}_{2}-{y}_{1})}^{2}}\\ =\sqrt{{(3-2)}^{2}+{(5-3)}^{2}}\\ =\sqrt{{\left(1\right)}^{2}+{\left(2\right)}^{2}}\\ =\sqrt{1+4}\\ =\sqrt{5}\end{array}$

Therefore, distance between the points $(2,3)$ and $(3,5)$ is width="26" style="max-width: none; vertical-align: -4px;" $\sqrt{5}$ units.

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