Question

Find the distance between the following points of the pair?

⇒ (2,3) , (4,1)

______________________
Use distance formula of coordinate geometry?

Answer 1

Given:-          

Let, the points be P(2,3) and Q(4,1)

So,

• ➸ x₁ = 2
• ➸ y₁ = 3
• ➸ x₂ = 4
• ➸ y₂ = 1

Formula Used:-          

~Distance formula

We can find out the distance between two points by using the Distance Formula.

• $\large\boxed{\tt{Distance\:=\:\sqrt{\:(x_{1}\:-\:x_{2} )^{2}\:+\:(\:y_{1}\:-\:y_{2}\:)^{2}\:\:\:\:\:}}}$

Where,

• ➸ x₁ = 2
• ➸ y₁ = 3
• ➸ x₂ = 4
• ➸ y₂ = 1

Solution:-        

Applying the distance formula:

➸ x₁ = 2

➸ y₁ = 3

➸ x₂ = 4

➸ y₂ = 1

$\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:(x_{1}\:-\:x_{2} )^{2}\:+\:(\:y_{1}\:-\:y_{2}\:)^{2}\:\:\:\:\:}}$

$\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:(\:2\:-\:4\: )^{2}\:+\:(\:3\:-\:1\:)^{2}\:\:\:\:\:}}$

$\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:(\:-2\: )^{2}\:+\:(\:2\:)^{2}\:\:\:\:\:}}$

$\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:4\:+\:4\:\:}}$

$\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:8\:\:}}$

$\qquad\tt{:\implies\:Distance\:=\:2\:\sqrt{\:2\:\:}}$

Thus,

 The distance between P(2,3) , Q(4,1) is 2√2.

Answer 2

Answer:

This Your Ans

Step-by-step explanation:

         

Let, the points be P(2,3) and Q(4,1)

So,

➸ x₁ = 2

➸ y₁ = 3

➸ x₂ = 4

➸ y₂ = 1

Formula Used:-          

~Distance formula

We can find out the distance between two points by using the Distance Formula.

\large\boxed{\tt{Distance\:=\:\sqrt{\:(x_{1}\:-\:x_{2} )^{2}\:+\:(\:y_{1}\:-\:y_{2}\:)^{2}\:\:\:\:\:}}}Distance=(x1−x2)2+(y1−y2)2

Where,

➸ x₁ = 2

➸ y₁ = 3

➸ x₂ = 4

➸ y₂ = 1

Solution:-        

Applying the distance formula:

➸ x₁ = 2

➸ y₁ = 3

➸ x₂ = 4

➸ y₂ = 1

\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:(x_{1}\:-\:x_{2} )^{2}\:+\:(\:y_{1}\:-\:y_{2}\:)^{2}\:\:\:\:\:}}:⟹Distance=(x1−x2)2+(y1−y2)2

\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:(\:2\:-\:4\: )^{2}\:+\:(\:3\:-\:1\:)^{2}\:\:\:\:\:}}:⟹Distance=(2−4)2+(3−1)2

\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:(\:-2\: )^{2}\:+\:(\:2\:)^{2}\:\:\:\:\:}}:⟹Distance=(−2)2+(2)2

\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:4\:+\:4\:\:}}:⟹Distance=4+4

\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:8\:\:}}:⟹Distance=8

\qquad\tt{:\implies\:Distance\:=\:2\:\sqrt{\:2\:\:}}:⟹Distance=22

Thus,

 The distance between P(2,3) , Q(4,1) is 2√2.