Question

Find the distance between the points, A(2a,6a) and B(2a+√3a , 5a).

Answer 1

Answer:

Step-by-step explanation:

By distance formula,

The distance between the points, A(2a,6a) and B(2a+√3a , 5a)

                              $=\sqrt{((2a+\sqrt{3}a)-2a)^2+(5a-6a)^2 } \\\\=\sqrt{(\sqrt{3}a)^2+(-a)^2} \\\\=\sqrt{3a^2+a^2} \\\\=\sqrt{4a^2} \\\\=2a$

Answer 2

To find:

Distance between the points, A(2a,6a) and B(2a+√3a , 5a)

Solution:

Distance between two points (x1,y1) and (x2,y2) is given as

$\sqrt{ {(x1 - x2) }^{2} + {(y2 - y2)}^{2} }$

Similarly,

Distance between two points A(2a,6a) and B(2a+√3a , 5a) =

$\sqrt{ {(2a - 2a - \sqrt{3}a ) }^{2} + {(6a - 5a)}^{2} } \\ = \sqrt{3 {a}^{2} + {a}^{2} } \\ = \sqrt{4 {a}^{2} } \\ = 2a \:$

Hence,

Distance between two points A(2a,6a) and B(2a+√3a , 5a) is 2a