Question

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

Answer 1

`\displaystyle\boxed{\rm \: Distance= \underline{\underline{√(13)}}}`

OR in Decimal,

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

Explanation:

Given:

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

To Find:

The Distance of the two given points

Solution:

To Find the distance between two points, we will use the distance formula, 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) }`

[Follow PEMDAS rule while simplifying]

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

`\rm \: Distance= √((3 * 3) + (2 * 2))`

`\rm \: Distance= √(9 + 4)`

`\rm \: Distance= √(13)`

`\rm \: Distance= {3.605}`

Hence, the distance between the two given points would be
`√(13)` or
`3.605`.

`\rule{225pt}{2pt}`

I hope this helps!

Have a good day! :)

[Desmos Graph solution is attached]