Math Help - Analytic Geometry Q7

1. Analytic Geometry Q7

Question:
Determine if the lines passing through the given pairs of points are parallel, perpendicular or intersect obliquely.

(a) $(1,-1)$ , $(-4,-4)$ and $(1,1)$ , $(4,-4)$
(b) $(-6,-4)$ , $(22,8)$ and $(-5,7)$ , $(7,8)$

Attempt:

(a)
Slope of : $(1,-1)$ , $(-4,-4)$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4-(-1)}{-4-1} = \frac{3}{5}$

Slope of : $(1,1)$ , $(4,-4)$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4-1}{4-1} = -\frac{5}{3}$

The lines are perpendicular to each other. We can prove it by using $m_1 \times m_2 = -1$.

(b)
Slope of : $(-6,-4)$ , $(22,8)$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-(-4)}{22 - (-6)} = \frac{3}{7}$

Slope of : $(-5,7)$ , $(7,8)$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-7}{7-(-5)} = \frac{1}{12}$

It is an intersect obliquely.

2. Why do you doubt? Did you make any errors deliberately?

You seem to have this unit. Move on to the next one.

By the way, very clean and very readable. Keep up the good notation!

3. Originally Posted by TKHunny
Why do you doubt? Did you make any errors deliberately?

You seem to have this unit. Move on to the next one.

By the way, very clean and very readable. Keep up the good notation!
Hi TKHunny, Thanks!

The problem is that I didn't attend the class. I only have the exercises with No Working and No Final Answer.

4. Originally Posted by looi76
Hi TKHunny, Thanks!

The problem is that I didn't attend the class. I only have the exercises with No Working and No Final Answer.
Well, if you have some doubt, make a sketch and see if your answer looks plausible
Especially in analytical geometry, it's easy to check.

If you want a software to draw points and lines, use Geogebra, it's pretty good !