# Math Help - Analytic Geometry Q8

1. ## Analytic Geometry Q8

Question:
The line through the points $(4,3)$ and $(-6,0)$ intersects the line through $(0,0)$ and $(-1,5)$. Find the angles of intersection.

Attempt:

Slope of line: $(4,3)$ and $(-6,0)$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0-3}{-6-4} = \frac{3}{10}$

Slope of line: $(0,0)$ and $(-1,5)$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5-0}{-1-0} = -5$

Angles of Intersection:

$m_1 = \frac{3}{10}$ , $m_2 = -5$

$\tan\phi = \frac{m_1 + m_2}{1 + m_1\cdot m_2} = \frac{\left(\frac{3}{10}\right) + (-5)}{1 + \left(\frac{3}{10}\right)\cdot(-5)} = \frac{47}{5}$

$\tan\phi = \frac{47}{5}$

$\phi = \tan^{-1}\left(\frac{47}{5}\right)$

$\phi = 84^o$

$\psi = 180^o - 84^o$
$\psi = 96^o$

So, the Angles of Intersection are $84^o$ and $96^o$. Am I right?

2. I don't understand how you can be that deliberate, accurate, and readable and not know if you are correct. Check you work. Check your intermediate steps. Check your assumptions. Did you use the tangent sum formula instead of the tangent difference formula? Go through it carefully and you tell you if it is correct.

3. Originally Posted by TKHunny
I don't understand how you can be that deliberate, accurate, and readable and not know if you are correct. Check you work. Check your intermediate steps. Check your assumptions. Did you use the tangent sum formula instead of the tangent difference formula? Go through it carefully and you tell you if it is correct.
I think its correct, but I need someone to look at it to be 100% sure.

4. You must be a bundle of nerves after an exam.

Why not just go with confidence?

Your style is too easy to follow for you still to lack confidence. Workings that cannot be followed do not provide confidence. Your workings? Different story.

Why do you think you can achieve 100% confidence? Give that up.