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Eddi Din [679]
2 years ago
15

Find the distance between two points: (5,3),(8,5)​

Mathematics
1 answer:
kozerog [31]2 years ago
5 0

Answer:

\displaystyle\boxed{\rm \: Distance= \underline{\underline{\sqrt{13}}}}

<em>OR </em><em>in </em><em>Decimal</em>,

\boxed{\rm \: Distance=\underline{\underline{3.605}}}

Step-by-step explanation:

<u>Given:</u>

Two points, that is (5,3) & (8,5)

<u>To Find:</u>

The Distance of the two given points

<u>Solution:</u>

To Find the distance between two points, we will use the <u>distance</u> <u>formula</u>, i.e. :

\boxed{ \rm \: Distance =  \sqrt{(x_2 - x_1) {}^{2}  + (y_2 - y_1) {}^{2} } }

According to the Question,

\rightarrow \:  \rm \: x_2 = 8

\rightarrow \:  \rm \: x_1 = 5

\rightarrow \:  \rm \: y_2 = 5

\rightarrow \:  \rm \: y_1 = 3

Now Substitute the values on the formula of Distance and then Simplify:

\rm \: Distance= \sqrt{(8 - 5 )^{2}  + (5 - 3) {}^{2} }

<em>[Follow PEMDAS rule while simplifying]</em>

\rm \: Distance= \sqrt{3 {}^{2}  + 2 {}^{2} }

\rm \: Distance= \sqrt{(3 \times 3) + (2 \times 2)}

\rm \:  Distance= \sqrt{9 + 4}

\rm \: Distance= \sqrt{13}

\rm \: Distance= {3.605}

Hence, the distance between the two given points would be \sqrt{13} or 3.605.

\rule{225pt}{2pt}

I hope this helps!

Have a good day! :)

<em>[Desmos Graph solution is attached]</em>

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