Question

0. Find the distance between the following pairs of points :
(7,-3); (-5, 2)
​

Answer 1

Distance Between Two Points is given by :

$\sf{\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}$

⇒ Distance Between (7 , -3) and (-5 , 2)  ​= $\sf{\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}$

⇒ Distance Between (7 , -3) and (-5 , 2)  ​= $\sf{\sqrt{\left(-5-7\right)^{2}+\left(2-(-3)\right)^{2}}}$

⇒ Distance Between (7 , -3) and (-5 , 2)  ​= $\sf{\sqrt{\left(-5-7\right)^{2}+\left(2+3\right)^{2}}}$

⇒ Distance Between (7 , -3) and (-5 , 2)  ​= $\sf{\sqrt{\left(-12\right)^{2}+\left(5\right)^{2}}}$

⇒ Distance Between (7 , -3) and (-5 , 2)  ​= $\sf{\sqrt{144\:+\:25}}$

⇒ Distance Between (7 , -3) and (-5 , 2)  ​= $\sf{\sqrt{169}}$

⇒ Distance Between (7 , -3) and (-5 , 2)  ​= 13 units

Answer 2

Answer:

The distance between the given points is 13 units.

Step-by-step-explanation:

We have given the coordinates of two points.

We have to find the distance between these two points.

Let the given points be A and B respectively.

A ( 7, - 3 ) ≡ ( x₁, y₁ )

B ( - 5, 2 ) ≡ ( x₂, y₂ )

Now, by distance formula,

d ( A, B ) = √[ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]

⇒ d ( A, B ) = √{ [ 7 - ( - 5 ) ]² + ( - 3 - 2 )² }

⇒ d ( A, B ) = √[ ( 7 + 5 )² + ( - 5 )² ]

⇒ d ( A, B ) = √[ ( 12 )² + 25 ]

⇒ d ( A, B ) = √( 144 + 25 )

⇒ d ( A, B ) = √169

⇒ d ( A, B ) = 13 units

∴ The distance between the given points is 13 units.

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Additional Information:

1. Distance Formula:

The formula which is used to find the distance between two points using their coordinates is called distance formula.

• d ( A, B ) = √[ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]

2. Section Formula:

The formula which is used to find the coordinates of a point which divides a line segment in a particular ratio is called section formula.

• x = ( mx₂ + nx₁ ) / ( m + n )

• y = ( my₂ + ny₁ ) / ( m + n )