Question

The angle between the line joining the points (1,0), (0,1) and the line x+2y-7=0 is​

Answer 1

Required angle is sin⁻¹ (1/3)

Step-by-step Explanation:

The given points are (1, 0) and (0, 1)

Then the slope of the line joining these points be

= (1 - 0)/(0 - 1) = - 1

The given line is

x + 2y - 7 = 0

or, 2y = - x + 7

or, y = (- 1/2) x + 7/2

So (- 1/2) is the slope of this line.

Therefore the angle between the given lines is

= sin⁻¹ [{- 1/2 - (- 1)}/{1 + (- 1/2) (- 1)}]

= sin⁻¹ [(- 1/2 + 1)/(1 + 1/2)]

= sin⁻¹ [(1/2) / (3/2)]

= sin⁻¹ (1/3)