Question

Find distance between point A (-1,2) & B(2,3)

Answer 1

${\underline{\sf{Question}}}$

Find distance between point A (-1,2) & B(2,3)

${\underline{\sf{Theory}}}$

Distance between two points :

The distance between any two points in the plane is the length of the line segment joining them.

The distance between two points P $\sf\:x_{1},y_{1}$ and Q $\sf\:x_{2},y_{2}$ is given by

$\sf\:PQ=\sqrt{(x_{2}-x_{1}){}^{2}+(y_{2}-y_{1}){}^{2}}$

${\underline{\sf{Solution}}}$

We have to find distance between A( -1,2) and B (2,3)

The distance between A and B

= Length of AB

$\sf = \sqrt{(2 - ( - 1)) {}^{2} + (3 - 2) {}^{2} }$

$\sf = \sqrt{3 {}^{2} + 1 {}^{2} }$

$\sf= \sqrt{ 9 + 1} = \sqrt{10}$

Hence ,the distance between A and B is √ 10 units .

Answer 2

Step-by-step explanation:

Find distance between point A (-1,2) & B(2,3)

{\underline{\sf{Theory}}}

Theory

Distance between two points :

The distance between any two points in the plane is the length of the line segment joining them.

The distance between two points P \sf\:x_{1},y_{1}x

1

,y

1

and Q \sf\:x_{2},y_{2}x

2

,y

2

is given by

\sf\:PQ=\sqrt{(x_{2}-x_{1}){}^{2}+(y_{2}-y_{1}){}^{2}}PQ=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

{\underline{\sf{Solution}}}

Solution

We have to find distance between A( -1,2) and B (2,3)

The distance between A and B

= Length of AB

\sf = \sqrt{(2 - ( - 1)) {}^{2} + (3 - 2) {}^{2} }=

(2−(−1))

2

+(3−2)

2