Question

Find the distance between the points A (2, -3) and B (-2.0)​

Answer 1

✪ Given :-

• Coordinates of A = ( 2 , - 3 )
• Coordinates of B = ( - 2 , 0 )

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✪ To Find :-

• Distance between the points A and B

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✪ Solution :-

By using distance formula

$\red \bigstar \: \boxed{ \green{\bf Distance = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } }}$

Here

• x₁ = 2
• x₂ = - 2
• y₁ = - 3
• y₂ = 0

Substitute values in formula

$\longmapsto \sf Distance = \sqrt{ {( - 2 - 2)}^{2} + {(0 + 3)}^{2} }$

$\longmapsto \sf Distance = \sqrt{ {( - 4)}^{2} + {(3)}^{2} }$

$\longmapsto \sf Distance = \sqrt{16 + 9}$

$\longmapsto \sf Distance = \sqrt{25}$

$\longmapsto \boxed{ \sf Distance = 5 \: unit}$

Answer 2

Topic:-

Co-Ordinate System

Question:-

Find the distance between the points A (2, -3) and B (-2,0)

Solution:-

A=(2,-3)

B=(-2,0)

Have To Find the distance between A and B

Let,

x1= 2 , y1 = -3

x2= -2 , y2= 0

So By applying distance formula we get

$\sqrt{(x1 - x2 {)}^{2} + (y1 - y2 {)}^{2} }$

$= \sqrt{( 2 - ( - 2) {)}^{2} + ( - 3 - 0 {)}^{2} }$

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

$= \sqrt{ {4}^{2} + 9 }$

$= \sqrt{16 + 9}$

$= \sqrt{25}$

$= 5$

Answer:-

The distance between A and B = 5

Formula Used:-

$\sqrt{(x1 - x2 {)}^{2} + (y1 - y2 {)}^{2} }$

More Information:-

Distance formula:-

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

Centroid formula:-

$\bf\dfrac{x_1+x_2+x_3}{3},\bf\dfrac{y_1+y_2+y_3}{3}$

Section formula Internal division

$\bf\dfrac{mx_2+nx_1}{m+n}, \bf\dfrac{my_2+ny_1}{m+n}$

Section formula External division

$\bf\dfrac{mx_2-nx_1}{m-n}, \bf\dfrac{my_2-ny_1}{m-n}$