[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex]\large\underline{ \boxed{ \sf{✰\:Important\: points }}}[/tex]
➢ Here question is asking to find the distance between points "A" and "B"
➢we can easily solve such ques by understanding a simple concept of Euclidean distance formula
➢ DISTANCE FORMULA :- Any algebraic expression that gives the distance between two points in a particular coordinate system in a particular number of dimensions
[tex]\rule{80mm}{2.5pt}[/tex]
[tex]{ \boxed{✜\underline{ \boxed{ \sf{Distance \: Formula = \sqrt{{(x_2 - x_1)}^{2} + {(y_2 - y_1) }^{2} } }}}✜}}[/tex]
★ Here
- [tex] \sf \:➣ x_2 = 7 \\ [/tex]
- [tex] \sf➣x_1=3[/tex]
[tex]\rule{80mm}{2.5pt}[/tex]
[tex] \large\underline{ \boxed{ \sf{✰\:Now\: substitute\:value}}}[/tex]
[tex]\sf \: ➛ \: distance = \sqrt{{(x_2 - x_1)}^{2} + {(y_2 - y_1) }^{2}} \\ \sf \: ➛distance = \sqrt{{(7 - 3)}^{2} + {(8 - 4) }^{2}} \\ \sf ➛solving \: bracket\\ \sf \: ➛distance =\sqrt{{(4)}^{2} + {(4) }^{2}} \\ \sf \: ➛solving \: square \: roots \\ \sf \: ➛distance = \sqrt{32} \\ \sf \: ➛distance = \sqrt{16 \times 2} \\ \sf \: ➛distance = \sqrt{4 \times 4 \times 2} \\ \sf \: ➛distance =4 \sqrt{2} units[/tex]
[tex]\rule{80mm}{2.5pt}[/tex]
Hence distance of AB =
[tex]{ \boxed{✟\underline{ \boxed{ \sf{\: AB=4 \sqrt{2}units {\green ✓}}}}✟}}[/tex]
Hope it helps !
