Question

Find the angle between the x -axis and the line joining the points (3, –1) and (4, –2).

Answer 1

The given points are ( 3,−1 ), and ( 4,−2 ).

The formula of slope of a line passing through two different points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by,

m= y 2 − y 1 x 2 − x 1 (1)

Substitute the values ( 3,−1 ), and ( 4,−2 ) for ( x 1 , y 1 ) and ( x 2 , y 2 ) in equation (1).

m= −2−( −1 ) 4−3 = −2+1 1 =−1

Now the formula for the slope of a line subtending an angle θ with the positive direction of x-axis in anticlockwise direction is given by,

m=tanθ(2)

Substitute the value of m in equation (3).

tanθ=−1 =−tan45° =tan( 180°−45° ) tanθ=tan135°

Compare both hand side for the value of θ,

θ=135°

Thus, the angle between the x-axis and the line joining the points ( 3,−1 ), and ( 4,−2 ) is 135°.