# Thread: Stuck on this question.

1. ## Stuck on this question.

I just can't work it out, can someone please post how to solve it:

If line1(l1) is a line through (3,-2) and (6,1) and line2(l2) is a line through (2,0) which makes an angle at 45 degree with the positive x-axis then are l1 and l2 parallel?

2. Originally Posted by JohnLord123
I just can't work it out, can someone please post how to solve it:

If line1(l1) is a line through (3,-2) and (6,1) and line2(l2) is a line through (2,0) which makes an angle at 45 degree with the positive x-axis then are l1 and l2 parallel?

Join (3,-2) to (6,1).
Draw a right-angled triangle using the point (6,-2).

$\theta$ is the acute angle at the (3,-2) vertex.

The perpendicular sides of the triangle have lengths 6-3=3 and 1-(-2)=3.

(6,1) is 3 units above (6,-2).

$tan\theta=1$

$\theta=45^o$

3. Or (pretty much the same thing): $\frac{y_2- y_1}{x_2- x_1}= \frac{1- (-2)}{6- 3}= \frac{3}{3}= 1$. Since that is equal to the tan(45), the two lines make the same angle with the x-axis and so are parallel.