Question

Find the angle between the line joining the points( 1,3)and (4,5)

Answer 1

QuesTion :-

→Find the angle between the line joining the points ( 1 , 3 ) and ( 4 , 5 ) .

AnsWer :-

$\to \boxed{ \theta = { \tan}^{ - 1} ( \frac{2}{3} )}$

To Find :-

→ Angle between line joining the given points .

Formula used :-

$\rm \mapsto slope \: (m) = \tan \theta \: \\ \\ \rm line \: joining \: the \: points \:(x_1 , y_1 ) and \\ \rm(x_2 , y_2) \: \: then \: its \: slope \: is - \\ \mapsto \boxed{ \rm \: slope \: (m) = \frac{y_2- y_1}{x_2 - x_1 \: } }$

Solution :-

According to the question,

→ Line joining the points (1,3) and (4,5)

$\to \rm \: x_1 = 1 , y_1 = 3 \\ \rm \to \: x_2 = 4 , y_2 = 5 \\ \\ \sf \: hence \\ \\ \to \rm \: slope(m) = \: \frac{y_2- y_1}{x_2 - x_1 \: } \: \: \\ \\ \to \rm tan \theta = \frac{ 5 - 3}{4 - 1} \\ \\ \to \rm \: \tan \theta = \frac{2}{3} \\ \\ \to \boxed{ \theta = { \tan}^{ - 1} ( \frac{2}{3} )}$