# What is the distance between  (2, 5)  and  (–7, 8) ?

Dec 7, 2015

$d \approx 9.49$ to 2 decimal places

$d = 3 \sqrt{10} \textcolor{w h i t e}{\ldots .} \textcolor{b l u e}{\text{exactly!}}$

#### Explanation:

Let the distance between be d

Let $\left({x}_{1} , {y}_{1}\right) \to \left(2 , 5\right)$
Let $\left({x}_{2} , {y}_{2}\right) \to \left(- 7 , 8\right)$

$\textcolor{b r o w n}{\text{Using Pythagoras:}}$

${d}^{2} = {\left(\text{difference in x")^2 +("difference in y}\right)}^{2}$

${d}^{2} = {\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}$

${d}^{2} = {\left(- 7 - 2\right)}^{2} + {\left(8 - 5\right)}^{2}$

${d}^{2} = {\left(- 9\right)}^{2} + {\left(3\right)}^{2}$

${d}^{2} = 81 + 9 = 90$

$d = \sqrt{90}$

$d \approx 9.49$ to 2 decimal places
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More accurately

$d = \sqrt{9 \times 10}$

$d = \sqrt{{3}^{2} \times 10}$

$d = 3 \sqrt{10} \textcolor{w h i t e}{\ldots .} \textcolor{b l u e}{\text{exactly!}}$