Question

The coordinates of point A are (-4,0) and the coordinates of point B are (0,3). Find the distance between these two points.

Answer 1

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The distance between two points (-4,0)≡(x1,y1) and (0,3)≡(x2,y2) is given by

d=√(x2−x1)²+(y2−y1)2²

⇒d=√(-4−0)²+(0−(+3))²

⇒d=√-16+9

⇒d=-7

⇒d=-7 units

Answer 2

Given:-        

The points are A( -4,0 ) and B( 0,3 )  

So,  

• ➸ x₁ = -4
• ➸ y₁ = 0
• ➸ x₂ = 0
• ➸ y₂ = 3

Formula Used:-          

~Distance formula  

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

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

Where,  

• ➸ x₁ = -4
• ➸ y₁ = 0
• ➸ x₂ = 0
• ➸ y₂ = 3

Solution:-        

Applying the distance formula:

➸ x₁ = -4  

➸ y₁ = 0

➸ x₂ = 0  

➸ y₂ = 3

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

$\qquad\tt{:\implies\:Distance\:=\:\sqrt{[(\:0\:-\:(-4)\:]^{2}\:+\:(\:3\:-\:0\:)^{2}\:} }$

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

$\qquad\tt{:\implies\:Distance\:=\:\sqrt{\:(16\:+\:9)\:} }$

$\qquad\tt{:\implies\:Distance\:=\:\sqrt{25} }$

$\qquad\tt{:\implies\:Distance\:=\:5\:units}$

Thus,  

The distance between A(-4,0) and B(0,3) is 5 units.