Question

The slope of a line is double of the slope of another line. If tangent of the angle between them is, find the slopes of he lines.

Answer 1

Let be the slopes of the two given lines such that.

We know that if θisthe angle between the lines l₁ and l₂ with slopes m₁ and m₂, then.

It is given that the tangent of the angle between the two lines is.

Case I

If m = –1, then the slopes of the lines are –1 and –2.

If m =, then the slopes of the lines areand –1.

Case II

If m = 1, then the slopes of the lines are 1 and 2.

If m =, then the slopes of the lines are.

Hence, the slopes of the lines are –1 and –2 or and –1 or 1 and 2 or.