A line passes through the points A(4, -6) and B(-2, -5). Show that the line AB makes an obtuse angle with the x-axis.

Question

Philoid · Accepted Answer

For the line to make an obtuse angle with X-axis, the angle of the line should be greater than 90

For the angle to be greater than 90°, tanθ must be negative

Where tanθ is the slope of the line.

Given points are A(4, -6) and B(-2, -5)

The slope of line AB is

Which is less than 0, hence negative.

,tanθ is negative in 2^nd quadrant whose angle is >90°.

So line AB makes obtuse angle(>90) with the X-axis.