Math, asked by dharmunamberdar, 1 month ago

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

Answers

Answered by SachinGupta01
10

 \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.

━━━━━━━━━━━━━━━━━━━━━━━━

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)

Similar questions