Question

A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.​

Answer 1

Answer:

The Intercept is the length of the point of intersection from the origin where the line cuts the coordinate axes.

Since the line cuts at 3 units from origin in both direction, there are various cases of the inclination.

Case (i): If it cuts in the first quadrant, the points are: (0,3) and (3,0).

Therefore the inclination would be: Difference in ordinates divided by Difference in abscissa values.

⇒ Inclination = Tan Ф = ( 3 - 0 ) / ( 0 - 3 )

⇒ Tan Ф = - 3 / 3 = -1

Hence the angle is -45 degrees.

Case (ii): If it cuts in the second quadrant, the points are: (0,3) and (-3,0)

Therefore the inclination would be:

⇒ Tan Ф = ( 3 - 0 ) / ( 0 - (-3) )

⇒ Tan Ф = 3 / 3 = 1

Therefore the angle is 45 degrees.

Similarly, Case (iii) would be third quadrant where the points are (-3,0) and (0,-3). Case (iv) would fourth quadrant where the points are (0,-3) and (3,0)

Cases where both the points have negative values will have Tan Ф = -1 and where both the points have positive and negative values, they will have Tan Ф = 1.

Hence the inclination where Tan Ф = -1 is -45 degrees and where Tan Ф = 1 is +45 degrees.