# What is the distance between (23,43) and (34,38)?

Jul 10, 2018

See a solution process below:

#### Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2}}$

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{34} - \textcolor{b l u e}{23}\right)}^{2} + {\left(\textcolor{red}{38} - \textcolor{b l u e}{43}\right)}^{2}}$

$d = \sqrt{{11}^{2} + {\left(- 5\right)}^{2}}$

$d = \sqrt{121 + 25}$

$d = \sqrt{146}$

Or, approximately:

$d \cong 12.083$

Jul 11, 2018

$\approx 12.08$

#### Explanation:

The key realization is that we can use the distance formula

$\sqrt{{\left(\Delta x\right)}^{2} + {\left(\Delta y\right)}^{2}}$

Where the Greek letter Delta means "change in". We just need to figure out how much our $x$ and $y$ change by, respectively.

We go from $x = 23$ to $x = 34$, so we can say $\Delta x = 11$.

We go from $y = 43$ to $y = 38$, so we can say $\Delta x = - 5$.

Plugging these into our formula, we get

$\sqrt{{\left(11\right)}^{2} + {\left(- 5\right)}^{2}}$

$\implies \sqrt{121 + 25} = \sqrt{146} \approx 12.08$

Hope this helps!