Question

Find the distance between two points A(1,2) and B(1, 3)​

Answer 1

$\large{ \underline{ \sf Solution - }}$

Given there are two points in the coordinate plane such that,

• A = (1,2)
• B = (1, 3)

To find the distance between them.

We know that,

Distance between two points is given by,

$\sf \implies \underline{ \boxed{ \sf D = \sqrt{ {(x_{2} - x _{1}) }^{2} + {(y _{2} - y_{1})}^{2} }}}$

Here, we have,

$\sf \implies x_1 = 1$

$\sf \implies x_2 = 1$

$\sf \implies y_1 = 2$

$\sf \implies y_2 = 3$

Substituting the values,

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

$\sf \implies \sf D = \sqrt{ {(0) }^{2} + {(1)}^{2}}$

$\sf \implies \sf D = \sqrt{ 0 + 1}$

$\sf \implies \sf D = \sqrt{1}$

$\sf \implies \sf D = \pm 1$

Distance is never negative,

$\sf \implies \sf Hence, \: D = 1$

Hence, required distance between the points is 1 units.

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Know more formulae :

➢ Section formula Internal division :

$\sf \implies\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

➢ Section formula External division :

$\sf \implies\left(\dfrac{mx_2-nx_1}{m-n},\dfrac{my_2-ny_1}{m-n}\right)$

➢ The mid point formula :

$\sf \implies \left( \dfrac{x_1 + x_2}{2} ,\dfrac{y_1 + y_2}{2} \right)$

➢ Centroid formula :

$\sf \implies\left(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)$