Answer:
[tex] \displaystyle\boxed{\rm \: Distance= \underline{\underline{\sqrt{13}}}} [/tex]
OR in Decimal,
[tex] \boxed{\rm \: Distance=\underline{\underline{3.605}}}[/tex]
Step-by-step 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. :
[tex] \boxed{ \rm \: Distance = \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } }[/tex]
According to the Question,
[tex] \rightarrow \: \rm \: x_2 = 8[/tex]
[tex]\rightarrow \: \rm \: x_1 = 5[/tex]
[tex]\rightarrow \: \rm \: y_2 = 5[/tex]
[tex]\rightarrow \: \rm \: y_1 = 3[/tex]
Now Substitute the values on the formula of Distance and then Simplify:
[tex] \rm \: Distance= \sqrt{(8 - 5 )^{2} + (5 - 3) {}^{2} } [/tex]
[Follow PEMDAS rule while simplifying]
[tex] \rm \: Distance= \sqrt{3 {}^{2} + 2 {}^{2} } [/tex]
[tex] \rm \: Distance= \sqrt{(3 \times 3) + (2 \times 2)} [/tex]
[tex] \rm \: Distance= \sqrt{9 + 4} [/tex]
[tex] \rm \: Distance= \sqrt{13} [/tex]
[tex] \rm \: Distance= {3.605} [/tex]
Hence, the distance between the two given points would be [tex]\sqrt{13}[/tex] or [tex] 3.605 [/tex].
[tex] \rule{225pt}{2pt}[/tex]
I hope this helps!
Have a good day! :)
[Desmos Graph solution is attached]
