Question

2- If A=(3, 4) and B = (7,8), find AB.​

Answer 1

`\huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }`

`\large\underline{ \boxed{ \sf{✰\:Important\: points }}}`

➢ 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

`\rule{80mm}{2.5pt}`

`{ \boxed{✜\underline{ \boxed{ \sf{Distance \: Formula = \sqrt{{(x_2 - x_1)}^(2) + {(y_2 - y_1) }^(2) } }}}✜}}`

★ Here

• 
  `\sf \:➣ x_2 = 7 \\`
• 
  `\sf➣x_1=3`

• 
  `\sf➣y_2=8`

• 
  `\sf➣y_1=4`

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`\large\underline{ \boxed{ \sf{✰\:Now\: substitute\:value}}}`

`\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 = √(32) \\ \sf \: ➛distance = √(16 * 2) \\ \sf \: ➛distance = √(4 * 4 * 2) \\ \sf \: ➛distance =4 √(2) units`

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Hence distance of AB =

`{ \boxed{✟\underline{ \boxed{ \sf{\: AB=4 √(2)units {\green ✓}}}}✟}}`

Hope it helps !

Answer 2

Use distance formula and take this question down, easily.

Explanation:

Distance xy =

`\sqrt{ {(x_2 - x_1) }^(2) + {(y_2 - y_1)}^(2) }`

Therefore AB

=
`√((7-3)^2 +(8-4)^2)`

=
`√((4)^2 +(4)^2)`

=
`√(32)`

=
`\boxed{4 √(2)-units}`