Question

Find the distance between the following pairs of points:

(2, 3), (4, 1)

Find the distance between the following pairs of points:

A (2, 3), B (4, 1) 

Answer 1

l  = ${\displaystyle \sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}}$

= ${\displaystyle \sqrt{{(4-2)}^2+{(1-3)}^2}}$

 = ${\displaystyle \sqrt{2^2+{(-2)}^2}}$

= ${\displaystyle \sqrt{4+4}}$

= ${\displaystyle \sqrt{8}}$

= ${\displaystyle \sqrt{4\times 2}}$

= ${\displaystyle 2\sqrt{2}}$ units

Answer 2

A (2, 3), B (4, 1)

Suppose the coordinates of point A are (x₁, y₁) and those of point B are (x₂, y₂).

x₁ = 2, y₁ = 3, x₂ = 4, y₂ = 1

According to distance formula,

d(A,B) = ${\displaystyle \sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}}$

d(A,B) = ${\displaystyle \sqrt{{(4-2)}^2+{(1-3)}^2}}$

d(A,B) = ${\displaystyle \sqrt{2^2+{(-2)}^2}}$

d(A,B) = ${\displaystyle \sqrt{4+4}}$

d(A,B) = ${\displaystyle \sqrt{8}}$

d(A,B) = ${\displaystyle \sqrt{4\times 2}}$

d(A,B) = ${\displaystyle 2\sqrt{2}}$

The distance between points A and B is ${\displaystyle 2\sqrt{2}}$ units.