Question

the distance between the points 3,-2 and -3,2 is ​

Answer 1

Step-by-step explanation:

answer is √52

we should use the formula √(x2-x1)+(y2-y1)

then we should substitute the value then we will get the answer .

Hope it's helpful to you

Answer 2

Distance between the points AB = √52 (or) 2√13

Step-by-step explanation:

★ Given that,

• A(3, -2)
• B(-3, 2)

★ To find,

• Distance between the points AB.

★ Formula,

$\boxed{ \large{\underline{\rm{\red{ Distance : \sqrt{ (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} }}}}}$

★ Let,

• x1 = 3 ; y1 = - 2
• x2 = - 3 ; y2 = 2

$\sf \implies AB = \sqrt{(-3-3)^{2} + (2-(-2))^{2}}$

$\sf \implies AB = \sqrt{(-6)^{2} + (2+2)^{2}}$

$\sf \implies AB = \sqrt{(-6)^{2} + (4)^{2}}$

$\sf \implies AB = \sqrt{36 + 16}$

$\sf \implies AB = \sqrt{52} \: \: (or) \: \: 2 \sqrt{13}$

$\underline{\boxed{\rm{\purple{\therefore Distance\:between\:AB : \sqrt{52} \:(or)\:2\sqrt{13}.}}}}\:\orange{\bigstar}$

★ Related formulae :

$\bigstar \boxed{\large{\underline{\rm{\red{ Mid-Point : \Bigg ( \cfrac{x_{1} + x_{2}}{2} , \cfrac{y_{1} + y_{2}}{2} \Bigg) }}}}}$

$\bigstar \boxed{\large{\underline{\rm{\red{ Section\:Formula : \Bigg( \cfrac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} , \cfrac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}} \Bigg) }}}}}$

$\bigstar \boxed{\large{\underline{\rm{\red{ Area\:of\:Triangle : \triangle = \cfrac{1}{2} \Bigg | x_{1}(y_{2} - y_{3}) + x_{2}(y_{3} - y_{1}) + x_{3}(y_{1} - y{2}) \Bigg |}}}}}$

$\bigstar \boxed{\large{\underline{\rm{\red{ Slope = \cfrac{y_{2} - y _ {1}}{x_{2} - x_{1}}}}}}}$

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